Hiddink will succeed Luiz Felipe Scolari, who was sacked on Monday.
The Dutchman will combine the Chelsea job with his current role as Russia boss.
“Chelsea Football Club is delighted to confirm Guus Hiddink will become temporary coach until the end of the season,” read an official club statement.
“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.”
“We talked about it and I thought about it,” Hiddink told Sky Sports News.
“It is for the period until the end of the English season.
“We are now preparing for the Azerbaijan game in March and then Finland in June, and there will be no damage for the Russian national team.”