Wright-Phillips, 25, had a similar move to Reading cancelled two weeks ago because of a knee injury.
But the former Southampton forward has seen another specialist, who has given him the all-clear to play again.
Reading have since signed Hereford United striker Mathieu Manset.
As gutted as I am that he's now gone, it was always going to happen and to be honest we needed to sell him
plymouthbornandbred
The signing is Chris Powell's first since becoming Charlton boss last week.
The new Addicks manager told the club website: "I am very happy to have a player of his calibre joining our squad."
Wright-Phillips, who has scored 13 goals this season, said: "I'm delighted to join Charlton.
"They're a club which I'm sure is heading in the right direction and, as soon as I spoke to the manager, I knew I wanted to be a part of it."
Source: BBC Sport
Source: BBC Sport