The 19-year-old is yet to feature for the Hoops, but he played 14 times for Greenock Morton on loan in 2013/14 and had a further spell with Dumbarton last season, where he made a further 15 appearances.
Kilmarnock boss Gary Locke said of the player: "Stuart has played for Scotland through the age grades and has stood out. I have watched him a lot, he is a left centre-back who is quick, he will have a lot to offer our team."
Findlay added: "Killie have given me this opportunity and I want to do well for them. I felt I played well in the Championship last season and now I am ready to make the step up and show what I can do at the top level."