The 24-year-old is the Canaries' third summer signing of the window after snapping up Burnley defender Ben Gibson and Greek left-back Dimitrios Giannoulis from PAOK Salonika, who were both on loan at the club last season.
Rashica his double digit goal tallies in all competitions for the German side in the 2018-19 season and the 2019-20 campaign, but an injury-hit spell last time limited his total to just three in the league last term.
Farke revealed that several "top clubs" were interested in the Kosovo forward and promised Rashica is able to "do something outstanding in the attack".
He added: "With Milot we have a very interesting player and we're delighted to have been able to bring him to Norwich City.
"Many top clubs have been interested in his signature over the last seasons and he was quite often connected with a big money move.
"He has delivered many end products and although he is young, he has played many games at the top level.
"He's a player who can do something outstanding in the offense. We also got the feeling from his age, ability, potential and personality that he will fit in quite well to our group. We hope that he can improve our offensive game.
"He can play a number of positions, as a winger, striker or number ten. He's a pretty versatile player and we're happy to be able to bring a quality player in."