The 19-year-old Ivorian will become Hoops boss Brendan Rodgers's first recruit of the January transfer window, subject to the granting of a visa.
Eboue, who has made 18 appearances in Russia's top flight this season and broken into the Ivory Coast senior setup, has signed a four-year deal at Celtic Park.
"A fee has been agreed with FC Krasnodar, as have personal terms with the player," a club statement reads.
"We have received the necessary governing body endorsement from the Scottish FA and subject to the visa being granted, Kouassi will join Celtic on a four-year contract."
Previous reports have suggested that Eboue will cost Celtic around £3m.