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And Tuchel, who was sacked by PSG in December 2020, emerged as the leading favourite to become the new Chelsea head coach.
Speaking to Chelsea's official website, Tuchel said: "I would like to thank Chelsea FC for their confidence in me and my staff.
"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 will take his first training session at Cobham this evening and will be in the dugout for the visit of Wolves on Wednesday evening.
The 47-year-old German spent two seasons at Borussia Dortmund and won the German Cup before switching to PSG in 2018.
Tuchel replaced Unai Emery at the Parisian club and continued PSG's dominance over the French league.
The new Chelsea boss won Ligue 1 twice, the Coupe de France and French League Cup during his two years at PSG.
Tuchel almost landed PSG their long-sought-after Champions League silverware last season as he took the defending French champions to the final.
Lampard, who was appointed Chelsea boss in 2019, left Stamford Bridge with the unfortunate honour of holding the worst Premier League points-per-match record for any manager under Roman Abramovich.
The 42-year-old Chelsea legend led the Blues to a fourth-place finish in the league last season and reached the FA Cup final.
Abramovich said that the former Chelsea midfielder would "always be warmly welcomed back at Stamford Bridge," despite the "difficult decision" in his dismissal.
The 54-year-old Chelsea owner said in a statement: "This was a very difficult decision for the club, not least because I have an excellent personal relationship with Frank and I have the utmost respect for him.
"He is a man of great integrity and has the highest of work ethics. However, under current circumstances we believe it is best to change managers.
"On behalf of everyone at the club, the board and personally, I would like to thank Frank for his work as head coach and wish him every success in the future.
"He is an important icon of this great club and his status here remains undiminished. He will always be warmly welcomed back at Stamford Bridge."
Featured Image Credit: PA
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