Having represented England at U18 and U20 level, Kieran won the last of his five Scotland caps as a replacement against Tonga in November.
"I'd love to play for Scotland again and playing with the Warriors will hopefully help," he said.
"I've spent my whole career at London Irish and I'll be sad to leave, but this is an exciting opportunity."
Glasgow head coach Gregor Townsend said: "Kieran has come through the academy system at London Irish and has worked hard to play at the highest level of the game.
"He is a physical, athletic second-row who can also play in the back-row, so he'll provide more competition and give us more options in the back five for next season."