"The Chelsea board would like to place on record our gratitude for his time as manager."
Scolari signed a lucrative three-year deal when he joined Chelsea and the London club could face a hefty compensation pay-out to their former manager.
Scolari's spokesman Acaz Felleger said it was Chelsea owner Roman Abramovich who had run out of patience with the Brazilian coach.
"It seems that Abramovich made the decision," Felleger told Lance newspaper's website.
"Scolari was not in a comfortable situation despite having the support of the squad and Peter Kenyon."
Felleger added that Scolari had paid the price for not being given the backing to refresh the aging Chelsea squad.
"The Chelsea squad are old. Felipe tried to rejuvenate it, but unsuccessfully. He asked (the board) to sign Deco and Robinho, but they only brought Deco."
Watch Scolari's last BBC interview
Scolari indicated he would give his version of events in the near future.
"I am thankful for the opportunity to have worked for Chelsea and in English football," Scolari said.
"It was a very valuable experience. I am sorry that my time with everyone could not last longer. I wish Chelsea luck in the three competitions they are participating in.
"I want to take the opportunity to inform that I will keep living in London. I will respond to the media soon."
Scolari's former team travel to Watford in the FA Cup fifth round on Saturday.
The tie at Vicarage Road is the start of a vital 11 days for Chelsea, with a crucial Premier League clash with third-placed Aston Villa on 21 February, followed by the visit of Juventus to Stamford Bridge in the Champions League four days later.
LUIZ FELIPE SCOLARI FACTFILE
1948: Born 9 November in Passo Fundo, Rio Grande do Sul
1999: Wins Copa Libertadores for a second time - with Palmeiras
2001: Replaces Emerson Leco as Brazil coach
June 2002: Brazil win the World Cup for a fifth time
Dec 2002: Takes over as Portugal manager
2004: Portugal lose to Greece in final of Euro 2004
2006: Pulls out of the running to succeed Sven-Goran Eriksson as England manager
2006: Leads Portugal to World Cup semi-finals
1 July 2008: Takes over as manager of Chelsea
9 Feb 2009: Sacked after draw with Hull sees Chelsea slip to fourth in the Premier League
Chelsea's official statement indicated that the club were eager to get a new man in charge for that run of games.
"Felipe has brought many positives to the club since he joined and we all feel a sense of sadness that our relationship has ended so soon," read the statement.
"Unfortunately the results and performances of the team appeared to be deteriorating at a key time in the season.
"In order to maintain a challenge for the trophies we are still competing for we felt the only option was to make the change now.
"The search for a new manager has already started and we hope to have someone in place as soon as possible."
Scolari won the World Cup as manager of his home country, Brazil, in 2002. He arrived at Chelsea following a six-year spell in charge of Portugal, who he led to the final of Euro 2004 and the semi-finals of the 2006 World Cup.
The 60-year-old made an impressive start but results deteriorated and of his 36 games in charge, 20 were won, five lost and 11 drawn.
Chelsea, who were unbeaten in the league at home for 86 matches until Liverpool's 1-0 win in October 2008, have lost two home league matches and drawn on five occasions this season, and were knocked out of the Carling Cup by Burnley on penalties.
Their record against the so-called big four this season is poor - they drew 1-1 at home with Manchester United and lost 3-0 away, were beaten 2-1 at home by Arsenal, and home and away by Liverpool.
United boss Sir Alex Ferguson, who has been at the helm at Old Trafford since 1986, said he felt a large degree of sympathy for Scolari.
"It is a sign of the times," Ferguson told MUTV.
"There is absolutely no patience in the world now. There was great expectation at Chelsea that they were going to do well this year - and it is only this last month they have had a bad spell.
"The judgment really is only on the last month."
Chelsea owner Roman Abramovich has now overseen the departure of four managers since his arrival in 2003.
Timing of sacking makes sense - Venables
Claudio Ranieri was sacked in 2004, Jose Mourinho in September 2007 and Grant in May 2008.
A banner unfurled during Chelsea's 0-0 draw with Hull at Stamford Bridge on Saturday called for the return of former Blues favourites Gianfranco Zola, currently in charge at West Ham, and Roberto Di Matteo, the MK Dons boss.
Chelsea were booed off the field at the final whistle and sections of the crowd could be heard chanting "you don't know what you're doing" at Scolari.
Several names have already joined Zola and Di Matteo in being linked with the vacancy, including Russia boss Guus Hiddink and former Barcelona boss Frank Rijkaard.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.