The Dutchman managed Australia at the 2006 World Cup in Germany and has also managed South Korea, Russia and his home country of Holland.
The official account of the Socceroos tweeted: "Our former boss has taken charge at @ChelseaFC - Good luck Guus! #GoSocceroos."
It will be Hiddink's second spell at Stamford Bridge after he managed them on a similar short-term deal in 2009.
He won over the Chelsea fans and delivered an FA Cup victory before returning to his international job with Russia at the end of that season.
Mourinho was sacked after clashing with angry players at the training ground.
AXED: Mourinho was sacked after nine defeats in 16 Premier League matches
Starsport understands furious Blues stars hit back after two days of being slated publicly by their then-boss.
Hiddink's first game in charge for the club could be
against Sunderland at Stamford Bridge on Saturday or the Boxing Day
clash with Watford.
