A--- Allah's Messenger (Peace be upon him) says: "I do not know when will I be dead, so follow the two who come after me.” He pointed to Abu Bakr and 'Umar (May Allah be pleased with them). (AtTirmidhi, Ibn Majah, Ahmed and AI-Hakim)

Narrated Hudhaifah (May Allah be pleased with him): "... 'Umar said: 'I did not mean that but I asked about that affliction which will spread like the waves of the sea.’ I (Hudhaifah) said: 'O leader of the faithful believers! You need not be afraid of it as there is a closed door between you and it.’ 'Umar asked, 'Will the door be broken or opened?' I replied, 'It will be broken.’ 'Umar said: 'Then it will never be closed again.’ (Sahih Bukhari)

The whole Ummah unanimously agreed on his right to be the successor of Abu Bakr (May Allah be pleased with them)