The 69-year-old also managed the Blues on a temporary basis for the final three months of the 2008-09 campaign.
"I am excited to return," said the Dutchman. "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."
Mourinho was sacked on Thursday with champions Chelsea 16th in the Premier League table, one point above the relegation zone.
Hiddink watched Saturday's visit of Sunderland from the stands, sat next to Chelsea owner Roman Abramovich and former Blues striker Didier Drogba.
Coaches Steve Holland and Eddie Newton were in charge of the team for the game against the Black Cats.
"It's a fantastic appointment. I'm very happy about it. This club needs an experienced manager at the helm and Guus Hiddink is clearly that," said Holland.
Chelsea technical director Michael Emenalo said a "palpable discord between manager and players" had contributed to Mourinho's dismissal, the second time he has been sacked by the club.
Bayern Munich manager Pep Guardiola, who is set to reveal on Saturday if he will stay at the German club beyond the end of the season, is among the possible permanent replacements.
Atletico Madrid's Diego Simeone and out-of-work Carlo Ancelotti, who managed Chelsea for two seasons from June 2009, have also been suggested as potential candidates for the full-time role.
A statement on the Chelsea website read: "The owner and the board welcome back a coach with a wealth of top-level experience and success, including his previous spell with the club in 2009 when we lifted the FA Cup.
"Mr Abramovich and the board believe that Guus has what it takes to get the best out of our talented squad."
Hiddink won six Dutch league titles and the European Cup in two spells as PSV Eindhoven manager. He has also coached South Korea, Australia and Russia.
He took over at Stamford Bridge in February 2009, replacing Luiz Felipe Scolari, and shared the role with his job as Russia manager.
Since then, he has endured unsuccessful spells as manager of Turkey, Russian side Anzhi Makhachkala and the Netherlands.
He stood down as Netherlands boss in June, during a miserable Euro 2016 qualifying campaign.
The Dutch failed to reach the finals, finishing fourth in their group behind Czech Republic, Iceland and Turkey.

The Northern Irish racer posted a lap of 123.650mph on his Classic Suzuki XR69 - in the best conditions of the week so far.
Michael Rutter, Ivan Lintin and Dean Harrison and James Hillier all posted laps in excess of 122mph.
Practice will continue on Thursday, with the start of racing on Saturday.
Bruce Anstey completed his first practice lap of the week (113.776mph) in the Lightweight class to sit just one second off Ian Lougher's fastest lap.
Following a red flag incident at Creg ny Baa and a short delay, Conor Cummins posted the quickest lap of the Classic TT session (107.199mph).
Dunlop also topped the Junior Classic timesheets with a lap of 102.082mph.
Isle of Man rider Andrew Dudgeon continued to set the pace in Manx Grand Prix qualification, the Ramsey man posting a time of 117.824mph on the GSX-R Suzuki he will ride in both the Junior and Senior MGP races.
Fellow Manx rider Michael Evans topped the MGP Newcomers A leaderboard with 112.591mph.
Due to a lack of practice time, Manx Grand Prix competitors will have practice on Thursday.
In the Newcomers A session three riders - Andrew Cuthbert (Sarah's), Shaun Wynne (Creg Ny Baa) and James Hinchcliffe (Graham's) - were to taken to hospital after separate crashes.
Michael Dunlop - 123.650mph
Ian Lougher - 113.893mph
John McGuinness - 107.199
Michael Dunlop - 102.082mph
Andrew Dudgeon - 117.824mph
Former Netherlands boss Guus Hiddink has been appointed interim Chelsea manager until the end of the season following the sacking of Jose Mourinho.
[NEXT_CONCEPT]
Michael Dunlop set the quickest time in qualifying at the 2016 Festival of Motorcycling for a third night in a row in the Isle of Man.