Former Chelsea and England midfielder Lampard was sacked on Monday, with the Blues ninth in the Premier League after five defeats in their last eight league matches.
Tuchel has signed an initial 18-month contract at Chelsea, and the German will get to work immediately.
“I would like to thank Chelsea for their confidence in me and my staff,” Tuchel told Chelsea’s official club website.
“We all have the greatest respect for Frank Lampard’s work and the legacy he created at Chelsea.
“At the same time I cannot wait to meet my new team and compete in the most exciting league in football.
“I am grateful to now be part of the Chelsea family – it feels amazing!”
Chelsea director Marina Granovskaia said: “It is never easy to change head coach in the middle of the season but we are very happy to secure one of Europe’s best coaches in Thomas Tuchel.
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“There is still much to play for and much to achieve, this season and beyond.
“We welcome Thomas to the club.”
Additional reporting by PA.