I asked Anas, "Was it a custom of the companions of the Prophet (ﷺ) to shake hands with one another?" He said, "Yes."
Sahih al-Bukhari Book 79, Hadith 37
← Previous Hadith The people of (the tribe of) Quraiza agreed upon to accept the verdict of Sa`d. The Prophet (ﷺ) sent for him (Sa`d) and he came. The Prophet (ﷺ) said (to those people), "Get up for your chief or the best among you!" Sa`d sat beside the Prophet (ﷺ) and the Prophet (ﷺ) said (to him), "These people have agreed to accept your verdict." Sa`d said, "So I give my judgment that their warriors should be killed and their women and children should be taken as captives." The Prophet (ﷺ) said, "You have judged according to the King's (Allah's) judgment." (See Hadith No. 447, Vol. 5)

Sahih al-Bukhari Book 79, Hadith 36 Next Hadith → We were in the company of the Prophet (ﷺ) and he was holding the hand of `Umar bin Al-Khattab.

Sahih al-Bukhari Book 79, Hadith 38