Hiddink, 69, had a caretaker spell in charge at Stamford Bridge in 2009 when Brazilian Luiz Felipe Scolari was fired and Chelsea went on to reach the Champions League semi-finals and win the FA Cup under his care.
"I am excited to return to Stamford Bridge. 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 said in a club statement.
His first priority will be to breathe life into Chelsea's Premier League campaign after the champions lost nine of their first 16 matches this season -- a calamitous run that ended with three-times title winner Mourinho's dismissal on Thursday.
Chelsea, embroiled in their worst start to a league season since 1978, were one point above the relegation zone ahead of Saturday's home clash with fellow strugglers Sunderland but responded with a 3-1 victory.
Hiddink watched from the stands with Mourinho's former assistants Steve Holland and Eddie Newton in charge for the day.
Mourinho was sacked for the second time as Chelsea manager on Thursday, seven months after leading them to the title.
The Portuguese was also fired in 2007, having won back-to-back league titles, after falling out with the club's billionaire Russian owner Roman Abramovich.
GREAT IMPRESSION
Since signing off from Chelsea with an FA Cup win over Everton, Hiddink has been manager of Turkey, Russian club side Anzi Makhachkala and most recently a dismal second spell as Netherlands coach which ended in his sacking after they failed to qualify for next year's Euro 2016 finals.
However, he made a great impression in his brief stay in London in 2009, proved popular with the Chelsea players and lost only one of his 22 games in charge.
He also helped Chelsea reach the Champions League semi-finals, losing narrowly to Barcelona, and has the chance to surpass that when the competition resumes in February with Chelsea through to the last 16 against Paris St Germain.
Hiddink has enjoyed an itinerant career that has included a spell at Real Madrid and national team roles with South Korea, Russia and Australia.
He took his first head coach's job at PSV Eindhoven in 1987 and won the Dutch title in three consecutive seasons as well as winning the European Cup in 1988.
After leaving PSV and joining Fenerbahce in 1990, he returned to the club in 2002 and won three more league titles in a four-year spell.
(Editing by Justin Palmer and Ken Ferris)
