The companions رضي الله عنهم of the Messenger of Allaah صلى الله عليه وسلم and those who came after them and followed their way, Ahlus-Sunnah wal-Jamaa'ah, are agreed that 'Uthmaan Ibn 'Affaan رضي الله عنه was the most qualified of people to become caliph after 'Umar ibn al-Khattaab رضي الله عنه, and no one objected or disagreed with that. Rather they all submitted to that because he was the best of Allaah's creation after the two Shaykhs, Abu Bakr رضي الله عنه and 'Umar رضي الله عنه, and a number of scholars of hadeeth and others narrated that there was consensus on the legitimacy of 'Uthmaan's caliphate after 'Umar رضي الله عنه. These reports include the following :
(1) - The report of Ibn Abi Shaybah رحمه الله with his isnaad going back to Haarith ibn Mudarrib رحمه الله who said: "I performed Hajj during the caliphate of 'Umar رضي الله عنه and they did not doubt that the caliphate would pass to 'Uthmaan رضي الله عنه after him." 
(2) - Abu Na'eem al-Asbahaani رحمه الله narrated with his isnaad going back to Hudhayfah رضي الله عنه that he said: "I was standing with 'Umar رضي الله عنه, my knee touching his knee, and he said: 'Who do you think the people will appoint?' I said: 'The people have already decided on Ibn 'Affaan.'" 
(3) - Al-Haafidh adh-Dhahabi رحمه الله narrated that Shareek ibn 'Abdillaah al-Qaadi رحمه الله said: "The Prophet صلى الله عليه وسلم died and the Muslims appointed Abu Bakr رضي الله عنه as his successor; if they had known that there was anyone better than him among them, then they would have deceived (the ummah, by doing that). Then Abu Bakr رضي الله عنه appointed 'Umar رضي الله عنه as his successor and was a man of truth and justice. When he was dying, he delegated the matter (of succession) to a council of six men, who agreed on 'Uthmaan رضي الله عنه. If they had known that there was anyone better than him among them, then they would have deceived us." 
All these reports clearly indicate that it was well established among the companions of the Prophet @ that 'Uthmaan رضي الله عنه was more qualfied to succeed to the caliphate when 'Umar ibn al Khattaab رضي الله عنه was still alive, because they already knew and had learned from the texts which spoke of his position in the order (of caliphs) that he would become caliph after 'Umar رضي الله عنه, and because they knew that he was the best of all the people after Abu Bakr and 'Umar (may Allaah be pleased with them both). 
(4) - Ibn Sa'd رحمه الله narrated with his isnaad going back to an-Nazzaal ibn Subrah رضي الله عنه who said: "'Abdullaah ibn Mas'ood رضي الله عنه said, when 'Uthmaan رضي الله عنه was appointed as caliph: 'We have appointed as caliph the best of those who are left, and we did not fail to select the best.'" 
(5) - al-Hasan ibn Muhammad al-Za'faraani said: "I heard ash-Shaafa'ee say: "The people were unanimously agreed on the caliphate of Abu Bakr رضي الله عنه, and Abu Bakr رضي الله عنه appointed 'Umar رضي الله عنه as his successor, then he delegated a council of six men to appoint one of their number, and they appointed 'Uthmaan (may Allaah be pleased with them all)."  Abu Haamid Muhammad al-Maqdisi narrated some words which he attributed to Imaam ash-Shaafa'ee: "You should know that the rightful ruler after 'Umar & was 'Uthmaan." 
That is because the members of the shoora council delegated the task of choosing the caliph to 'Abdur-Rahmaan ibn 'Awf رضي الله عنه and he chose 'Uthmaan رضي الله عنه, and the Sahaabah were unanimously agreed on that. The people approved of what 'Abdur-Rahmaan رضي الله عنه did, and 'Uthmaan رضي الله عنه led the people in the path of truth and ruled with justice until he was martyred. 
(6)- Ibn Taymiyah رحمه الله narrated that Imaam Ahmad said: "They did not all agree to swear allegiance to anyone as they all agreed to swear allegiance to 'Uthmaan." 
(7) - Abul-Hasan al-Ash'aree رحمه الله said: "The caliphate of 'Uthmaan رضي الله عنه after 'Umar رضي الله عنه is proven because he was chosen by the members of the shoora council who were appointed by 'Umar. They chose him and approved of his leadership, and they were unanimously agreed about his virtue and justice." 
(8) - 'Uthmaan as-Sabooni رحمه الله said, explaining the belief of the salaf and of the scholars of hadeeth concerning the order of the caliphs, after mentioning that they said that the caliphate of Abu Bakr رضي الله عنه came first, then 'Umar رضي الله عنه: "Then came the caliphate of 'Uthmaan رضي الله عنه by the consensus of the shoora council and all the Companions رضي الله عنهم of the Prophet صلى الله عليه وسلم and with their approval, thus he became the caliph who was in charge." 
(9) - Shaykhul-Islaam Ibn Taymiyyah رحمه الله said: "All the Muslims swore allegiance to 'Uthmaan رضي الله عنه and no one held back. When the prominent people and people of authority and power swore allegiance to him, he became the ruler. If 'Abddur-Rahmaan رضي الله عنه had sworn allegiance to him but 'Ali and other prominent and powerful Sahaabah رضي الله عنهم had not done so, he would not have become the ruler. But 'Umar رضي الله عنه appointed six men to the shoora council - 'Uthmaan رضي الله عنه, 'Ali رضي الله عنه, Talhah رضي الله عنه, az-Zubayr رضي الله عنه, Sa'd رضي الله عنه and 'Abdur-Rahmaan ibn 'Awf رضي الله عنه, then Talhah رضي الله عنه, az-Zubayr رضي الله عنه and Sa'd رضي الله عنه withdrew from the race willingly, leaving 'Uthmaan رضي الله عنه, 'Ali رضي الله عنه and 'Abdur-Rahmaan رضي الله عنه, who did not withdraw but he was delegated to select one of the other two. For three days during which 'Abdur-Rahmaan رضي الله عنه swore that he did not sleep much, he consulted the first Muslims and those who had followed them in truth. He consulted the commanders of the troops who had gone for Hajj with 'Umar رضي الله عنه that year. The Muslims suggested to him that 'Uthmaan رضي الله عنه should be appointed caliph, and he said that they all favoured 'Uthmaan رضي الله عنه, so they swore allegiance to him, not because of something that he gave them or because they were afraid of him. Hence more than one of the salaf and imams, such as Ayoob al-Sakhtiyaani, Ahmad ibn Hanbal, ad-Daaraqutni and others said: 'Whoever prefers 'Ali رضي الله عنه over 'Uthmaan رضي الله عنه has thought badly of the Muhaajireen and Ansaar رضي الله عنهم.' This is another sign of 'Uthmaan's superiority رضي الله عنه, because they appointed him as their leader willingly and on the basis of shoora." 
(10) - al-Haafidh Ibn Katheer رحمه الله narrated that there was consensus among the Sahaabah رضي الله عنهم about the appointment of 'Uthmaan رضي الله عنه as caliph and he reported that the members of the shoora council delegated the matter to 'Abdur-Rahmaan رضي الله عنه, for him to work out for the Muslims who was the best of them to be appointed to this position. He asked those whom he could ask of the shoora council members, and others, and they did not suggest anyone but 'Uthmaan ibn 'Affaan رضي الله عنه. He said to 'Ali رضي الله عنه: 'If I do not appoint you, who do you suggest?' He said: ''Uthmaan.' And he said to 'Uthmaan رضي الله عنه: 'If I do not appoint you, who do you suggest?' He said: 'Ali ibn Abi Taalib.' It seems that this was before the matter was limited to three people and 'Abdur-Rahmaan رضي الله عنه withdrew from the race in order to choose the best candidate.
Then 'Abdur-Rahmaan ibn 'Awf رضي الله عنه began to consult the people about these two and he collected the opinions of both the ordinary Muslims and their leaders, consulting them in groups and individually, secretly and openly, even consulting the women in seclusion from behind their curtains and asking the children in their schools. He even asked the travellers and Bedouin who came to Madeenah during those three days. He did not get much sleep, rather he spent his time in prayer and supplication, seeking guidance and asking wise people. He did not find anyone suggesting that anyone was better than 'Uthmaan ibn 'Affaan رضي الله عنه. On the fourth day after the death of 'Umar ibn al-Khattaab رضي الله عنه, he came to the house of his nephew al-Miswar ibn Makhramah and told him to call 'Ali رضي الله عنهand 'Uthmaan رضي الله عنهfor him. So he called them and they came to 'Abdur-Rahmaan رضي الله عنه. He told them that he had asked the people and he did not find anyone who suggested that anyone was better than either of them, then he took a solemn promise from each of them that if he was appointed he would be just, and if he was not appointed, that he would hear and obey.
Then he went out to the mosque, wearing the head cover that the Messenger of Allaah صلى الله عليه وسلمhad put on him, and with a sword by his side. He sent for the most prominent people among the Muhaajireen and Ansaar, and the call went out to the people at large: 'As-Salaatul-Jaami'ah (prayer is about to begin).' The mosque filled with people and was so crowded that 'Uthmaan رضي الله عنه could not find a place to sit except at the back, and he was a very shy man. 'Abdur-Rahmaan ibn 'Awf رضي الله عنه ascended the minbar of the Messenger of Allaah صلى الله عليه وسلم, where he stood for a long time and said a lengthy du'aa' that the people could not hear. Then he spoke and said: 'O people, I have asked you secretly and openly about your leader, and I did not find suggesting that anyone was better than either of these two men, 'Ali and 'Uthmaan. Come here, O 'Ali.'
He came and stood beneath the minbar, then 'Abdur-Rahmaan رضي الله عنه took him by the hand and said: 'Will you swear allegiance to me in accordance with the Book of Allaah and the Sunnah of His Prophet صلى الله عليه وسلم and the deeds of Abu Bakr and 'Umar?' He said: 'By Allaah, no, but on the basis of my efforts and ability (i.e., I will do my best).'
He let go of his hand and said: 'Come here, O 'Uthmaan. He took him by the hand and said: 'Will you swear allegiance to me in accordance with the Book of Allaah and the Sunnah of His Prophet صلى الله عليه وسلم and the deeds of Abu Bakr and 'Umar?' He said: By Allaah, yes.'
He looked up at the ceiling of the mosque, still holding 'Uthmaan's hand رضي الله عنه, and said: 'O Allaah, listen and bear witness; O Allaah, listen and bear witness; O Alaah, listen and bear witness. O Allaah, that which was on my shoulders I place on the shoulders of 'Uthmaan.'
The people crowded around, swearing their allegiance to 'Uthmaan رضي الله عنه, until they surrounded him beneath the minbar. 'Abdur-Rahmaan رضي الله عنه sat down where the Messenger of Allaah صلى الله عليه وسلم used to sit and 'Uthmaan رضي الله عنه sat beneath him on the second step, and the people came to him and swore allegiance to him, and 'Ali ibn Abi Taalib رضي الله عنه swore allegiance to him first - or it was said that he was the second to do so." 
These reports, all of which mention the consensus of all these leaders, offer definitive proof that the oath of allegiance to 'Uthmaan رضي الله عنه as caliph was done with the consensus of all the Sahaabah رضي الله عنهم and no one disagreed or objected to that.