Werner, who has scored 32 goals in 43 games this season, will remain in Leipzig for the rest of the Bundesliga season before joining Chelsea in July, subject to medical examination.
The 24-year-old made his international debut in 2017 and scored 72 goals in four seasons with Leipzig. Last November, he became the youngest player to make 200 appearances in the Bundesliga.
"I am delighted to be signing for Chelsea, it is a very proud moment for me to join this great club," said Werner.
"Of course I want to thank RB Leipzig, the club and the supporters, for four fantastic years. You will always be in my heart.
"I look forward to next season with my new teammates, my new manager and of course the Chelsea fans. Together we have a very successful future ahead of us."
Known for his rhythm and his clinical finish, Werner will join a strike force which also includes the French international Olivier Giroud and the English international Tammy Abraham.
He is Chelsea's second recruit before next season, alongside Ajax winger Hakim Ziyech.
"We are very pleased that Timo Werner has chosen to join Chelsea," said Chelsea director Marina Granovskaia.
"He is a player who was coveted all over Europe and it is not a surprise, he has this rare mixture of being young and exciting and yet established and experienced."
"We can't wait to have Timo on board, but until then we wish him and RB Leipzig all the best for the rest of the season."
