Frimpong returned from an anterior cruciate ligament injury that ruled him out for seven months in September but is yet to feature in a Premier League match for the Gunners this season.
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Earlier in November, Goal.com revealed that Arsenal would look to offload the 20-year-old in the January transfer window after the north London club opted not to open discussions over a new deal.
Frimpong's two appearances for Arsene Wenger's team in 2012-13 have both come in the Capital One Cup. He came off the bench in the 6-1 victory over Coventry before starting in the Gunners' topsy-turvy 7-5 win against Reading.
After making 14 appearances in all competitions for Arsenal last season, Frimpong joined Wolves on loan but played only five times before suffering the serious knee injury.
He joins Charlton on the back of their 1-0 victory over Burnley on Saturday. Chris Powell's team currently lie in 14th place in the Championship.