Jose Mourinho agreed a compensation package with Chelsea late on Thursday and said he was "proud" of what he had achieved with the London club.
Jose Mourinho is said to be relieved that he is leaving Chelsea
Mourinho was replaced by Avram Grant as Chelsea manager on Thursday after earlier parting company with the club.
And after spending several hours at Stamford Bridge, Mourinho and Chelsea came to an agreement on his contract.
A club statement read: "Chelsea FC has reached agreement on all contractual arrangements with Jose Mourinho."
Mourinho's three-year reign at Chelsea ended late on Wednesday when he left by "mutual consent" and was swiftly replaced by Grant.
I wish great success to the club, a club that will be forever connected to me for some historical moments
And after making an emotional farewell to the players at Chelsea's Cobham training ground he headed to Stamford Bridge, where he is thought to have agreed a severance package of about £20m for the remaining three years of his contract.
"I am very proud of my work in Chelsea Football Club and I think my decision in May 2004 to come to England was an excellent one," said Mourinho.
"It was a beautiful and rich period of my career. I want to thank all Chelsea FC supporters for what I believe is a never-ending love story.
"I wish great success to the club, a club that will be forever connected to me for some historical moments.
"I wish the players happiness in football and in their family life. Finally on my wife's and children' s behalf we thank the great professionalism of their school teachers and the beauty of so many friends."
Earlier on Thursday, Chelsea released an "open letter to their fans" to thank supporters for their "patience and understanding during what has been a difficult time".
The statement said: "The reason the decision has been taken is that we believed the breakdown [between Mourinho and owner Roman Abramovich] started to impact on the performance of the team.
"Recent results supported this view. We did not want this to continue or affect the club further."
The statement added: "It is only right that we explain the reasons behind Jose Mourinho leaving Chelsea and also recognise the immense contribution he has made to the club and to English football.
"Early this morning we announced that Chelsea and Jose Mourinho had agreed to part company by mutual consent.
"The key phrase here is that there was mutual agreement. Jose did not resign and he was not sacked.
Mourinho returned to Stamford Bridge on Thursday afternoon
"What is clear, though, is we had all reached a point where the relationship between the club and Jose had broken down. This was despite genuine attempts over several months by all parties to resolve certain differences."
And the club praised Mourinho for his achievements, which included winning successive Premier League titles.
"Chelsea's long-term football objectives and ambitions remain unchanged, and the appointment of Avram Grant and Steve Clarke is aimed at continuing to achieve those goals.
"We also must pay tribute to the great job Jose did for Chelsea. He has been the most successful manager the club has known and he rightly deserves that place in our history.
"Jose has been instrumental in putting Chelsea where it is today, among the leading clubs in European and world football.
"He will always be welcome at Stamford Bridge, whether as the guest of Chelsea or as the manager of another club, and he will be given the reception and respect his position in our history deserves."
Grant, 52, steps up to the role of Chelsea manager from director of football and will be assisted by Steve Clarke.
The Israeli is due to be unveiled at a news conference on Friday.
According to BBC football correspondent Jonathan Legard, Mourinho has felt a sense of relief since his departure.
"He's felt boxed-in from demands on high, he's felt boxed-in from the boardroom in terms of boardroom dealings," said Legard.
"And he's felt under pressure from those alongside him in the dugout, namely the man who has succeeded him, Avram Grant."
Chelsea also confirmed that Mourinho's backroom staff have left the club, including assistant managers Baltemar Brito and Rui Faria.
Head opposition scout Andre Villas and goalkeeping coach Silvino Louro have also departed Stamford Bridge.