The forward, 24, has agreed personal terms with the Blues and, subject to passing a medical, will join in July after the German league season ends.
Werner, who joined Leipzig from Stuttgart in 2016, has scored 32 goals in all competitions so far this season.
“I am delighted to be signing for Chelsea, it is a proud moment for me to be joining this great club,” said the German international.
Werner, who is known for his pace and can also play as a winger, thanked the club and fans at Leipzig and said they would “would always be in my heart”.
His July move also confirms Werner will not play for Leipzig in the Champions League quarter-finals in August.
He added: “I look forward to next season with my new team-mates, my new manager and of course the Chelsea fans.
“Together we have a successful future ahead of us.”
Chelsea director Marina Granovskaia says the club is “excited” to have one of Europe’s “most coveted players” heading to Stamford Bridge.
“He has that rare mix of being young and exciting and yet established and proven,” she added.
Werner is Chelsea’s second signing for next season after they completed a £37m deal for Ajax winger Hakim Ziyech in February