The 35-year-old former England defender has been a free agent since being released from his contract with League Two side Notts County in December.
And after a trial period and practice match, Gunners boss Arsene Wenger has signed Campbell as defensive cover.
"He brings experience, good advice, and physically he has worked hard. We're giving him a chance," said Wenger.
"For us it is a good help until the end of the season, and for him it is a good opportunity to show he can still play in the Premier League."
Campbell will not be fit enough to feature in this weekend's match against Bolton, however, while Wenger has admitted the defender needs time to build up his match fitness.