Sayyiduna Ali (may Allah be pleased with him) said: When the House was demolished after Jurhum, Quraysh rebuilt it. When it came time to place the Black Stone, they quarrelled among themselves over who would place it, and they agreed that whoever first entered through this door would place it. Then the Messenger of Allah (peace and blessings be upon him) entered through the gate of Banu Shaybah. He (peace and blessings be upon him) called for a cloth, placed the stone in its middle, and ordered every clan to take hold of a part of the cloth and lift it, and the Messenger of Allah (peace and blessings be upon him) took it and set it in place.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9208
Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) narrated that when the Prophet (peace and blessings be upon him) came during the period of (the treaty with) Quraysh, he entered Makkah through this great door, while Quraysh were sitting on the side of the Black Stone.
It has also been narrated from Ibn Umar as a marfu' report that he (the Prophet) entered through the gate of Banu Shaybah and left through the gate of al-Hannatin, but its chain is not mahfuz (preserved).
Ata' (may Allah have mercy on him) says: The muhrim may enter from wherever he wishes. The Prophet (peace and blessings be upon him) entered through the gate of Banu Shaybah and left through the gate of Banu Makhzum towards al-Safa. This is a good mursal report.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 9209