The 58-year-old spent three months in charge of the Addicks at the end of the 2013-14 campaign, keeping the club in the Championship.
Since leaving The Valley the Belgian has spent time in charge of Blackpool, Standard Liege and Metz.
Riga replaces compatriot Karel Fraeye, who was sacked from his post as interim head coach on Wednesday.
Charlton are currently 23rd in the Championship table, three points from safety, and are on a run of 10 games without a win in all competitions.
Fraeye was appointed in late October following the departure of Guy Luzon, but only won two of his 14 matches in charge of the first team.
In a statement on the club website, Addicks owner Roland Duchatelet admitted the club had made errors in player recruitment and said the board of directors accepted responsibility for "a disappointing season".
"It was crucial we dealt with the position of the head coach," the Belgian businessman added.
"Jose did an excellent job in his short period with Charlton two seasons ago. He was very popular with supporters and I believe that he will get us back on track."
Riga won seven of his 16 games during his stint at The Valley in 2014 but left the south-east London club when his contract was not renewed that summer and joined Blackpool.
BBC Radio London's Andy Rowley
Charlton fans are increasingly angry with how the club is being run by Roland Duchatelet, who is now onto his sixth head coach since taking over the club in January 2014.
There have been a number of recent protests at The Valley aimed at Duchatelet and chief executive Katrien Meire from supporters, who have now come together to form a group called "Coalition Against Roland Duchatelet" in an attempt to bring about a sale of the club.
Riga has far more managerial experience than his predecessor Karel Fraeye but, given his previous links to Duchatelet and the antipathy towards the board of directors, the appointment could only serve to fan the flames for further supporter unrest.

Charlton Athletic supporter Daniel Boylett, 36, of Eltham, was arrested after trouble broke out at the match on 23 September 2015.
He was found guilty at Croydon Crown Court of attempted damage for the attack on Kayla. He was also found guilty of violent disorder.
Boylett was released on bail to be sentenced on 28 April.
Crystal Palace, who are nicknamed The Eagles, adopted Kayla as a mascot in 2010.
Who is Kayla the Eagle?
The court heard handler Chris Belsey was walking around the Selhurst Park pitch with the bird on his forearm at the game.
Prosecutor Daniel Higgins said "three or four fans were shouting abuse" at the pair when one leaned over the barrier and "threw a punch".
He said Mr Belsey did not know if the punch had landed and Kayla "seemed unhurt", but "due to her delicate bone structure if she had been hit with force, her bones could easily break".
Four other men were on trial with Boylett over the trouble which marred the Capital One third-round tie.
Mr Higgins said there had been trouble "before, during and after" the game.
The first scuffles broke out as police escorted Charlton supporters to Selhurst Park.
One officer suffered a cut lip after being hit by what he thought was a bottle as rival fans tried to break the police cordon, the court heard.
At the end of the match, which Charlton lost 4-1, Donegan ran at police wielding a large yellow cone and had to be "subdued with a baton strike".
After his arrest, he told police he was "annoyed" as "we just got battered. I picked it up and let my anger out".
The jury were previously directed to acquit Cowcher, Boylett, Kitto and McConville on another count of violent disorder due to insufficient evidence.

The 1920s window at St Paul's Church in Grangetown, Cardiff, depicts air, sea and land battles alongside religious images and trench scenes.
The church says the masonry around the window must be replaced.
Repairs could cost tens of thousands of pounds.
Championship strugglers Charlton Athletic have reappointed Jose Riga as head coach on an 18-month deal.
[NEXT_CONCEPT]
A football fan has been found guilty of trying to punch Crystal Palace's bald eagle mascot during a cup game
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An appeal has been launched to raise money to refurbish one of the largest stained-glass windows in Wales honouring casualties from World War One.