On Monday, it was revealed that two bids had been accepted for the 22-year-old, who only joined the Scottish Premiership side during the summer.
The former Tottenham Hotspur trainee has now agreed personal terms and passed a medical with Al Ahly, with his contract said to run until 2020.
His agent Lee Payne is quoted by Sky Sports News as saying: "Souleymane has always been fully committed to Kilmarnock, but once they agreed a fee, he was given permission to talk to the club.
"It was too good an offer for Kilmarnock to turn down, and Souleymane is extremely grateful to Kilmarnock for his time at the club.
"Al Ahly are one of the biggest clubs in that part of the world and are top of the Egyptian league. It is a club that match Souleymane's ambitions."
Coulibaly leaves Rugby Park having scored 11 goals in 26 appearances.