He had 23 goals and nine assists in 36 appearances for the Bundesliga side this past season, has been capped 10 times for France and will be Chelsea's first signing under new manager Mauricio Pochettino.
Chelsea did not reveal the financial details of the deal, but British media have reported that the fee was close to £60 million.
"I am incredibly happy to be joining Chelsea," Nkunku said in a statement.
"A big effort was made to bring me to the club and I am looking forward to meeting my new coach and team-mates and showing the Chelsea supporters what I can do on the pitch."
"Having played in Ligue 1 and the Bundesliga, I now want to play in the Premier League, one of the strongest leagues in the world. I am very excited for this challenge and will be proud to wear the Chelsea shirt."
The Stamford Bridge outfit will seek to revive their fortunes under former Tottenham Hotspur manager Pochettino after finishing 12th in the recently concluded campaign, their worst finish to a season since 1994.
