Fernando Torres will join Milan permanently on January 5 ahead of his expected return to Atletico Madrid.
Liverpool boss Brendan Rodgers has insisted Mario Balotelli will not be going out on loan in the January transfer window.
The fee for the highly-rated 22-year-old was not disclosed by Robins boss Derek McInnes is delighted with his new signing.
"He has accumulated quite a lot of games and experience in the Scottish Premier League and has been a key player for Kilmarnock over the last few seasons," he told the club's website.
"He has amassed quite a lot of Under-21 games for Scotland and is now involved in the full senior squad as well.
"He is 22 years of age and that is a good age for us, which is important. We think we have got a very good deal for the club, considering he only had six months of his contract left and a few other clubs were looking at him.
"Liam is someone we think will only get better. He gets around the pitch, utilises the ball well and takes responsibility for his position."
Kelly, who has one full Scotland cap to his name, was born in Milton Keynes and came through the Dons' academy before joining Kilmarnock and he became the midfield lynchpin at Rugby Park.
Kelly was part of the team which won the Scottish League Cup in March when Kilmarnock upset the odds with a 1-0 win over Celtic at Hampden Park but tragically his father died of a heart attack whilst watching the match.