The 21-year-old has decided to move to Rugby Park club in search of regular first-team football.
Ibrahim had other offers from Scottish Premier League clubs to go on loan, and the Nigerian also had the chance to move to Russia.
But the player, who has been included in Nigeria's preliminary squad for the Africa Cup of Nations, was persuaded to join the Ayrshire club by Killie boss Kenny Shiels.
"He's signed a two-year deal with us," said Shiels.
"I believe it's quite a coup for Kilmarnock and we are a good fit for him.
"Rabiu had an offer from a club in Russia but he and his advisors thought it would be better for his career development to stay in Scotland and they were equally as keen as we were for the deal to go through.
"We signed him on a free transfer. He's away with the Nigeria squad for the AfCon at the moment.
"I believe January 9 is the deadline for them to name their final squad. I would quite like him to be named in the squad for his confidence. If he is named then as soon as they go out of the competition he will join up with us."