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The Germany international will join at the end of the current Bundesliga season, and will become Chelsea’s second signing ahead of next campaign after Ajax's Hakim Ziyech.
"The 24-year-old has agreed personal terms with the Blues, and will remain at the German club for the rest of the Bundesliga season. He will link up with his new team-mates in July, subject to passing a medical examination," read a statement on the Chelsea website.
"One of the most feared young strikers in Europe, Werner is renowned for his pace, movement, link-up play and finishing ability. At Leipzig he has most often been deployed in a front two, but he can also play out wide in a front three or as the central striker.
"He is currently enjoying the most profitable season of his career yet, having already scored 32 goals and registered 13 assists in 43 appearances in all competitions. After finding the net again against Fortuna Dusseldorf last night, he has two games remaining this season to improve on those numbers."
Werner will link up with his new team-mates in July, subject to passing a medical examination.
He has even reportedly insisted on sitting out the remainder of Leipzig’s Champions League matches so as not to jeopardise his move to the Premier League.
“I am delighted to be signing for Chelsea,” Werner said. “It is a very proud moment for me to be joining this great club. I of course want to thank RB Leipzig, the club and the fans, for four fantastic years. You will forever be in my heart. I look forward to next season with my new team-mates, my new manager and of course the Chelsea fans. Together we have a very successful future ahead of us."