The Kosovo international has signed a four-year contract with the newly promoted Canaries.
Rashica has been brought in to replace Emiliano Buendia, who recently joined Aston Villa.
And the 24-year-old says he is excited to join his new club.
"I will of course give my best to this football club in every game and hope to excite the fans with many goals and assists. I can't wait to get started," he said.
"I know a few things about the club, particularly the style of play under Daniel Farke.
"I want to continue to learn and develop as a player and person and I think that the style of play here will suit me very well."