The Black Cats agreed a fee with Charlton on deadline day before completing the signing of the 25-year-old on a three-and-a-half-year deal.
Keane added: "It's always healthy to have competition for places in the squad. "I'm sure he'll do well for the club."
While Greg Halford has gone the opposite way, on loan to Charlton, Reid was Keane's fifth signing in January.
Addicks boss Alan Pardew had told the club's website: "It was a difficult decision, but we have to look at ourselves and say 'are we going to let this affect us or will this make us stronger'? Hopefully, the latter will happen."
Reid joined the Addicks from Tottenham in a move which could have amounted to £3million in August 2006, and has made 23 appearances so far this season.