Riga, the former Standard Liege boss, takes over from Powell with immediate effect and his first game in charge will be against Huddersfield Town on Wednesday.
The Belgian will be assisted by compatriot Karel Fraeye at The Valley as Charlton battle to avoid relegation from the Championship.
Riga is already well-known by the Charlton hierarchy, with club owner Roland Duchatelet also owning the Jupiler League side Standard Liege.
Charlton currently sit bottom of the league table, four points adrift of safety, but have three games in hand following their FA Cup run and postponements earlier in the season.
Powell was relieved of his duties earlier on Tuesday after a run of five defeats from Charlton's last six league matches and following elimination from the FA Cup on Sunday at the hands of Sheffield United.
The 44-year-old spent three years in charge at the club, having made over 200 appearances as a player.
