Rashica, who was linked with a move to Aston Villa has finally joined Daniel Farke's side following the relegation of Weder Bremen from the Bundesliga.
The attacking midfielder's recruitment serves as a replacement for Emiliano Buendia, who joins Aston Villa after playing a tremendous role in Norwich's qualification to the top-flight.
The 27-year-old was with joy after joining the Canaries.
"I’m really excited to play in front of the Norwich fans and in the Premier League," he said. "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.
"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.
“I have spoken with the boss and I know what he wants to see from me. Those conversations with him recently have been a big help and I am very excited.
“I don’t know any of the players or staff in the group, but I have a lot of friends in the game and here in Germany who speak very highly of Norwich City and how the club works.
"I’ve watched many Norwich City games in the Premier League. It has always been a dream, for me to play in the Premier League and I’m so happy that Norwich have given me this great opportunity.
“I’ve played a few games in England before. I played in a Europa League qualifier for Vitesse against Southampton, as well as a few pre-season fixtures against other English teams.
“I also have some close family in London. Me and my family are looking forward to moving to England, being closer to them and experiencing something new."
The Kosovo International made 87 Bundesliga appearances and scored 21 goals in four-and-a-half seasons with Bremen.
