The Finland internationalist was a success for the Rugby Park side after he arrived on loan during the 2010/11 season and had lost little of his popularity when he signed again in January.
The 31-year-old chose to leave as a free agent in the summer and had been training with former team FF Jaro in his homeland. Kilmarnock stayed in contact with the forward, though, and have convinced him to return on a new deal.
"We're absolutely delighted," said Allan Johnston, the Kilmarnock manager. We spoke to him early in pre-season to try and get him over and get something sorted so it's good it's finally done.
"Somebody with his quality will be a massive factor in how well we do this season. You saw the last couple of games of last season, the performances he put in."