The 36-year-old Norwegian, a Classics specialist who also has five Grand Tour appearances to his name, joins after one season at FDJ-BigMat.
Rasch said: "Team Sky were the number one team I wanted to join and I'm really happy to have signed. Next season I hope I can get into the Classics team because I have a lot of experience with that type of riding, and I'll be happy to work as a domestique during the stage races as well."
Team Sky race coach Rod Ellingworth said: "It's great to have Gabriel on board. Not only will he be a huge asset to us in the Classics, his attitude and experience will be of massive benefit to the team."