Werner, who has scored 32 goals in 43 appearances this season, passed the medical test and will remain with Leipzig for the remainder of the Bundesliga season before joining Chelsea in July.
The 24-year-old made his international debut in 2017 and netted 72 times in four seasons with Leipzig. Last November he became the youngest participant in over 200 appearances in the Bundesliga.
“I’m very happy to sign for Chelsea. I’m very proud to be joining this great club,” said Werner.
“I want to thank RB Leipzig, the club and the fans for four wonderful years. You will be in my heart forever.
“I’m looking forward to next season with my new teammates, my new manager and Chelsea fans. Together we have a very successful future ahead of us.”
Werner, known for his pace and clinical finishing, will join the strike force, including France international Oliver Giroud and England international Tommy Abraham.
He is Chelsea’s second signing ahead of next season alongside Ajax winger Hakim Ziek.
“We are very pleased that Timo Werner has chosen to join Chelsea,” said Chelsea Director Marina Granovsky.
“It’s no wonder he’s a favorite player across Europe and he has a rare mix of young and exciting and yet established and proven.
“We can’t wait to put Timo on board, but until then we wish him and RB Leipzig the best of luck for the rest of the season.”