A statement on the Blues's official website read: "Chelsea Football Club is delighted to confirm Guus Hiddink will become temporary coach until the end of the season. He is due to meet the players later this week.
"The club would like to take this opportunity to thank the Russian Football Union for their understanding and cooperation."
Earlier, the Dutchman had revealed that he was expecting to be in charge at Stamford Bridge next week.
The Blues only sacked Brazilian Luiz Felipe Scolari on Monday, and have been quick to make their move for the Dutchman, who has a close relationship with, Chelsea's Russian owner, Roman Abramovich.
"It's to help out a friend," Hiddink told Dutch Radio station 538. "Abramovich is doing so much for Russian football and I want to do something back.
"At the end of March there are two qualification matches, then again in June. So it is possible and at the end of the English season it's over. Within a few days I will go to London. I expect to be on the pitch next week."
Hiddink has experience of both managing a club and country at the same time, having previously coached PSV Eindhoven while helping steer Australia to the 2006 World Cup finals.
The Dutchman will not be in charge of the team for their FA Cup Fifth Round meeting with Watford on Saturday, although he will be in attendance at Vicarage Road ahead of taking over next week, and he plans to contact sacked manager Luiz Felipe Scolari to discuss the team.
"It's never enough time to prepare a team in one week but this is an exceptional situation. Chelsea have good players and they should be in top form and that should make my job easier," he told Reuters. "I haven't done it yet but I will call him [Scolari] in the next day or two."
Hiddink also revealed that he has not, and does not intend to sign a contract with the club, and will not be bringing in his own assistants straight away.
"I don't have to sign one. It's not a question of money," he said. "I always want to see the situation in the team myself first before making any changes if they have to be made."
His first match as manager will be at Villa Park when the Blues, currently fourth in the Premier League, visit third-placed Aston Villa, before welcoming Juventus - and former Chelsea coach, Claudio Ranieri - to Stamford Bridge for the first-leg of the Champions League last 16.
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