The 56-year-old, who was working as a technical director in AC Milan's youth academy, took the Addicks' training on Tuesday morning just hours after the sacking of manager Chris Powell.
Riga, who will be assisted by Karel Fraeye, will take charge of his first game when Huddersfield visit The Valley in the Sky Bet Championship on Wednesday night.
Riga has worked with Charlton owner Roland Duchatelet at Standard Liege - another club the Belgian businessman owns - having appointed him there in 2011.
He took Standard to the last 16 of the Europa League in his first season in charge and has also managed R.A.E.C
Mons.
Former England international Powell, who guided the Addicks to the League One title in 2012, was relieved of his duties on Tuesday morning despite revealing he had agreed financial terms on a new contract last week.
But he clashed with Duchatelet over the club's recruitment policy after the Belgian businessman brought in a host of foreign players in January from Standard - while selling key men such as Dale Stephens and Yann Kermorgant.
Former Addicks left-back Powell, 44, did not name a single one of those new players in his final starting line-up, Sunday's 2-0 FA Cup defeat at Sheffield United which signalled the end of his three-year reign.
Duchatelet said of Powell's exit: "We have been working with Chris Powell and his representatives for a couple of weeks to try to agree a contract extension which would have seen us continue to work together.
"There was good progress, but we could not reach an agreement over the club's football strategy going forward
"The situation put a strain on the working relationship between Chris and the board
Therefore I think it is best for all parties that we part ways at this stage.
"I would like to thank Chris for his commitment and hard work over the past three years
The club enjoyed a number of good times under his leadership.
"However, given the club's position in the league and the number of important fixtures upcoming, I felt this difficult decision was unavoidable at this time.
"I can assure supporters this was not an easy decision, but it has been made with the club's future in mind
Time will tell if it is the right decision."
Charlton are currently bottom of the Championship, four points adrift of safety, but their cup run and a spate of postponements means they have at least three games in hand on the clubs above them.
Riga could face anger from the terraces with fans unhappy at the decision to axe Powell and concerned that Charlton are becoming a feeder club to Standard Liege.
Powell's sacking also provoked criticism from his former players
Midfielder Stephens, who was sold to Brighton in January, said on Twitter: "This game is ruthless, can't say I'm surprised
No place for loyalty unfortunately, he deserved better."
Ex-Addicks goalkeeper John Sullivan wrote: "Absolutely shocking decision to sack Chris Powell
What he has achieved on the budget he's had is nothing short of sensational."
Source : PA
Source: PA