Narrated Abdullah ibn Abbas:The Prophet (ﷺ) wore the mantle under his right armpit with the end over his left shoulder, and touched the corner (Black Stone), then uttered "Allah is most great" and walked proudly in three circuits of circumambulation. When they (the Companions) reached the Yamani corner, and disappeared from the eyes of the Quraysh, they walked as usual; When they appeared before them, they walked proudly with rapid strides. Thereupon the Quraysh said: They look to be the deer (that are jumping). Ibn Abbas said: Hence this became the sunnah (model behaviour of the Prophet).
حَدَّثَنَا مُحَمَّدُ بْنُ سُلَيْمَانَ الأَنْبَارِيُّ، حَدَّثَنَا يَحْيَى بْنُ سُلَيْمٍ، عَنِ ابْنِ خُثَيْمٍ، عَنْ أَبِي الطُّفَيْلِ، عَنِ ابْنِ عَبَّاسٍ، أَنَّ النَّبِيَّ صلى الله عليه وسلم اضْطَبَعَ فَاسْتَلَمَ وَكَبَّرَ ثُمَّ رَمَلَ ثَلاَثَةَ أَطْوَافٍ وَكَانُوا إِذَا بَلَغُوا الرُّكْنَ الْيَمَانِيَ وَتَغَيَّبُوا مِنْ قُرَيْشٍ مَشَوْا ثُمَّ يَطْلُعُونَ عَلَيْهِمْ يَرْمُلُونَ تَقُولُ قُرَيْشٌ كَأَنَّهُمُ الْغِزْلاَنُ قَالَ ابْنُ عَبَّاسٍ فَكَانَتْ سُنَّةً .
AbuDaud
The Rites of Hajj (Kitab Al-Manasik Wa'l-Hajj) • Hadith 1889