The former Standard Liege boss will take the team for his first match when Huddersfield visit The Valley on Wednesday night.
The 56-year-old, who was working as a technical director in Milan's youth academy, took the Addicks' training on Tuesday morning just hours after the sacking of Powell.
Riga took Liege to the last 16 of the Europa League after winning their group two years ago.
Charlton have also appointed Karel Fraeye as assistant to Riga as the team prepares for the challenges of moving off the foot of the table and trying to avoid relegation into League 1.
A statement from Charlton read: "Jose Riga has been appointed as head coach of Charlton Athletic, the club confirmed on Tuesday afternoon.
"Riga will work alongside Karel Fraeye, who also joins as assistant head coach.
"Following the departure of Chris Powell, Riga becomes the 23rd man to take permanent charge of Charlton's first team."
Earlier, Belgian owner Roland Duchatelet said of his decision to part with Powell: "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."