The London club, owned by Russian billionaire Roman Abramovich, were given the go-ahead by Russian Football Union (RFU) on Tuesday.
"Chelsea Football Club can confirm it has officially approached the Russian Football Union (RFU) for permission to speak to Guus Hiddink to become the club’s temporary coach until the end of the season while continuing to be in charge of the Russian national team," Chelsea statement read.
"That permission has been granted and Chelsea would like to thank the RFU for their co-operation."
Hiddink's agent insisted earlier that his client is unlikely to leave Russia for Chelsea, but now the Dutchman can manage both sides without having to quit his original post.
The 62-year-old had a similar experience four years ago, when he was in charge of PSV Eindhoven besides the Australian national team.
Hiddink led PSV to back-to-back Eredivisie titles in 2005 and 2006, as well as guiding Australia to the 2006 World Cup for the first time.
Earlier reports in England tipped the ex-Holland boss as the number one candidate to take over at Stamford Bridge, thanks to his personal relationship with Abramovich.