Former Paris Saint-Germain coach Thomas Tuchel was among the frontrunners for the manager's post at Chelsea after Frank Lampard was sacked on Monday.
Lampard's departure after 18 months in charge followed a 3-1 win on Sunday over second division Luton Town in the FA Cup fourth-round.
"We are grateful to Frank for what he has achieved in his time as head coach of the club," Chelsea said in a statement.
"However, recent results and performances have not met the club's expectations, leaving the club mid-table without any clear path to sustained improvement."
Lampard, who replaced Maurizio Sarri as head coach in July 2019, is acknowledged as one of the club's greatest players.
During 13 years in west London, he lifted a dozen trophies including three Premier League titles as well as four FA Cups.
In 2012 he skippered the side to the Champions League trophy. A year later he was in the team which claimed the Europa League.
Club owner Roman Abramovich said: "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."
Tuchel was sacked in December four months after steering PSG to a domestic treble and the 2020 Champions League final.
Before taking over from Unai Emery at PSG in July 2018, he took Borussia Dortmund to the 2017 German Cup.
Lampard was the 10th full-time manager under Abramovich since the Russian billionaire bought the club in 2003.
"He is an important icon of this great club and his status here remains undiminished," added Abramovich. "He will always be warmly welcomed back at Stamford Bridge."