The Canaries, who are promoted to the Premier League, were on the hunt for a replacement for departed star Emi Buendia.
Now they have secured Kosovo international Rashica, who is only 24 and comes with an excellent reputation as a result of his exploits in the Bundesliga.
Rashica has spent the past three and a half years with Werder Bremen.
Farke told the Norwich website: "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.
"In Germany he spent his time with Werder Bremen, who were struggling a bit last season, but Milot is a player full of potential. He's quick and smart in his movements, technically good and great in finishing and assisting goals.
"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 offence. 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."