The experienced Dutch coach, 69, watched Chelsea's 3-1 win over Sunderland on Saturday, having resumed a role he previously performed in 2009, when he led the London club to glory in the FA Cup.
"I am excited to return to Stamford Bridge," Hiddink said in a statement on the Chelsea website before the game.
"Chelsea is one of the biggest clubs in the world, but is not where it should be at the moment. However, I am sure we can all turn this season around.
Hiddink sees Chelsea win, Norwich imperil Van Gaal
"I am looking forward to working with the players and staff at this great club and especially renewing my wonderful relationship with the Chelsea fans."
Mourinho, 52, was sacked by Chelsea for the second time on Thursday after a run of nine defeats in 16 games saw them slide towards the relegation zone.
With first-team coach Steve Holland taking charge of the team against Sunderland, Hiddink sat in an executive box alongside owner Roman Abramovich and former Chelsea striker Didier Drogba.
Chelsea captain John Terry welcomed Hiddink's return, telling Sky Sports: "Guus Hiddink's training is very intense. He is a great man manager as well."
Contenders to replace Mourinho at Chelsea
Abramovich previously turned to Hiddink in February 2009 after sacking Luiz Felipe Scolari.
In a statement, Chelsea said: "Mr Abramovich and the board believe that Guus has what it takes to get the best out of our talented squad."
Well travelled and vastly experienced, Hiddink began his coaching career with PSV Eindhoven and delivered the club's first ever European Cup success in 1988.
He has also managed Fenerbahce, Valencia, Real Madrid, Real Betis and Anzhi Makhachkala, as well as the national teams of the Netherlands, twice, South Korea, Australia, Russia and Turkey.
Chelsea bet on Hiddink to recapture Midas Touch
His most recent role, as Netherlands coach, came to an end in June after a poor start to qualifying for Euro 2016.
Hiddink's first game will be the Boxing Day fixture at home to Watford next Saturday, which is followed by a trip to Manchester United on December 28.
Writing in the match programme for the Sunderland game, Chelsea chairman Bruce Buck said the club had "anguished" over the decision to dismiss Mourinho "for some time".
"Please believe me when I say the decision was made for no reason other than to do what we believe is in the best interests of this club," he added.
"We are one of the biggest clubs in the world and we are all determined, as a collective unit, to get back to where we should be."
Chelsea technical director Michael Emenalo said "palpable discord between manager and players" was a factor in Mourinho's dismissal, but Terry said player unrest was not the reason for his departure.
"We are aware there have been rumours of player power at the club, but I want to make it clear that is not the case," Terry wrote in the programme.
"We leave all decisions to Mr Abramovich and the board, and know that our job, as players, is to focus on getting results on the pitch."
Mourinho attended the Championship match between Brighton and Hove Albion and Middlesbrough on Saturday in his first public appearance since his sacking.
Sporting a newly shaven head and wearing a dark jacket, he was photographed in a seat at the Amex Stadium, where his former Real Madrid assistant Aitor Karanka was taking charge of Middlesbrough, who won 3-0.
The agency that represents Mourinho said in a statement that he would not be taking a sabbatical and would be attending matches in order to provide support to his "friends" in the game.
"He will not be taking a sabbatical, he isn't tired, he doesn't need it, he is very positive, and is already looking forward," said a statement from CAA, which also said Mourinho would remain in London.
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