The German manager, 47, was confirmed on Tuesday January 26, as the successor to Frank Lampard, who was sacked on Monday.
In a statement, the club said Tuchel had signed an 18-month contract “with the possibility of an extension”.
Chelsea also confirmed that Tuchel will be in the Stamford Bridge dugout for Wednesday’s Premier League clash with Wolves.
“I would like to thank Chelsea FC for their confidence in me and my staff,” Tuchel told the 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 arrives at Chelsea having guided PSG to four major honours and the Champions League final during his time in the French capital.
Prior to that, he spent seven seasons coaching in the Bundesliga, first with Mainz, where he led them into the Europa League, and then a successful period with Borussia Dortmund where he won the German Cup.