The RB Leipzig star has finalised terms on a contract worth around £170,000 a week with the Premier League club which runs until 2025.
Werner will link up with his new team mates in July, subject to passing a medical.
The fee for the 24-year-old German international is understood to be around £48million.
It is a major coup for Frank Lampard, who will also welcome Ajax attacker Hakim Ziyech to the club this summer.
Werner, who had also been on Liverpool’s radar, has scored 32 times all competitions for RB Leipzig this season to enhance his reputation as one of the best attacking prospects in Europe.
Chelsea are backing boss Lampard heavily in the transfer market as they look to mount a title challenge to Liverpool and Manchester City next season.
Leicester City’s Ben Chilwell is understood to be next in Lampard’s sights after agreements were reached for Werner and Ziyech.
Bayer Leverkusen’s talented young midfielder Kai Havertz is also understood to be among Chelsea’s targets.
Lampard’s immediate focus will be on steering the club into the Champions League.
The Blues are currently sitting fourth in the table, three points ahead of Manchester United, and resume their season at Aston Villa on Sunday.