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 will get to work immediately.
Former Paris St Germain manager Tuchel took his first training session on Tuesday night and will be in charge for Wednesday’s home league clash with Wolves.
“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!”
Tuchel led PSG to the 2020 Champions League final, but was sacked by the French giants in December.
The 47-year-old will now be expected to revive Chelsea’s faltering campaign, unify a split dressing room – and seal a top-four Premier League finish to secure Champions League qualification.
Chelsea’s board were understood to have grown weary of perceived muddled thinking in Lampard’s changeable tactics, with the 42-year-old paying the price for failing to integrate the summer’s £220million-worth of new signings.
Chelsea owner Abramovich is understood to believe Tuchel’s experience in managing major egos and talents like Neymar and Kylian Mbappe will allow him to hit the ground running with the Blues.
Tuchel has been itching to get back to work after his December sacking by PSG, and his agent Pini Zahavi has successfully sung his praises to Abramovich.
“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,” said Chelsea director Marina Granovskaia.
“There is still much to play for and much to achieve, this season and beyond.
“We welcome Thomas to the club.”
Former Borussia Dortmund boss Tuchel must build a clear attacking strategy, find definitive roles for Timo Werner and Kai Havertz, tighten a tentative defence and also rebuild brittle collective confidence.
Chelsea’s all-time record goalscorer, Lampard took the helm as manager in 2019 in a move to thrill Blues fans.
Lampard belied the club’s transfer ban and previous paltry recruitment under Maurizio Sarri to seal a top-four Premier League finish in his first campaign, securing the all-important Champions League qualification.
Chelsea’s vast summer recruitment left Lampard with a bloated, imbalanced and callow squad however, and the Blues’ inconsistency ultimately led to his downfall.