The German joins on a 18-month contract with the possibility of an extension.
“There is still much to play for and much to achieve, this season and beyond. We welcome Thomas to the Club.”
Tuchel was sacked by PSG in December despite winning two Ligue 1 titles and after reaching the Champions League final in 2020.
Before his trophy-laden reign in France, Tuchel managed Borussia Dortmund in the Bundesliga where he won the German Cup in 2017.
The 47-year-old is now tasked with reviving a team that looks short on both leadership and confidence.
Tuchel also faces the task of replacing fan favorite Lampard who rejoined Chelsea as head coach in July 2019, enjoying a successful first season with the London club.
The former England international was also backed in the 2020 summer transfer window, recruiting big-money signings including German internationals Kai Havertz and Timo Werner.
After a strong start to the season, Tuchel takes over with the club languishing ninth in the Premier League following a run of five defeats in the past eight league games.
“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 will take training on Tuesday evening before leading his new team into Wednesday’s Premier League match against Wolves.