The 21-year-old has agreed a two-year contract with the Rugby Park club, which are currently sixth in the SPL log, after Celtic allowed the player to move on in search of regular first-team football.
Ibrahim had an offer from Russia and was also believed to be a loan target for other Scottish sides.
â€œHeâ€™s signed a two year deal with us,â€ Kilmarnock manager Kenny Shiels told STV.
â€œI believe itâ€™s quite a coup for Kilmarnock and we are a good fit for him.
â€œRabiu 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.
â€œWe signed him on a free transfer.â€
The former Golden Eaglets star will not join up with his new teammates immediately as he is currently with the Nigeria national team preparing for the 2013 Africa Cup of Nations.
â€œHeâ€™s away with the Nigeria squad for the AFCON at the moment,â€ Shiels said.
â€œI 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.
â€œIf he is named then as soon as they go out of the competition, he will join up with us.â€