The 24-year-old Ghanaian midfielder is waiting for a work permit to be approved to let him complete his move and will arrive for a medical next week.
Rubin fans have criticised the decision to loan him to the Hoops but the club's sporting director Ayrat Garayev said: "He wasn't getting games and asked to be allowed to leave.
"We then received the offer from Celtic, who have the advantage of playing in the Champions League. We could have insisted he stay but if a player decides he wants to leave, he is not worth keeping. So we wish him all the best."
Meanwhile, ex-Celtic starlet Islam Feruz has been shipped out on loan by Chelsea to the Russian second-division side Krylia Sovetov. The 18-year-old striker opted to sign a one-year deal with them rather than go to the English Championship.
In May, Feruz turned down the chance to play for Scotland Under-19s in their Euro Elite qualifiers. Instead he turned out for a Chelsea select in a sevens tournament in Hong Kong.