The 27-year-old left-back called time on his 13-year association with the Gunners in order to move to the Midlands on a four-year deal worth a reported £7m, having entered the final 12 months of his existing contract with Wenger's side.
"We didn't offer him a new deal and that's why he decided to go," Wenger confirmed at a press conference this morning ahead of the Baggies' trip to the Emirates on Monday night.
"It will be strange to see him in a different shirt, because he's a player who has been educated here from a very young age. I'm sure that he will have a great motivation and a huge influence at West Brom that he can give another push to his career."
Asked if he thought Gibbs had failed to realise his true potential at Arsenal, Wenger responded: "Look, he has become an England international here, he made a good career here and I believe that Arsenal is very proud of that and Kieran Gibbs can be proud.
"I think what happened to him, he has been bothered a few times when he wasn't in front of other players. Many times he was a regular player here, but he had some fitness worries as well."
Gibbs made 137 top-flight appearances during his time in North London but had just 11 outings in his final season with the club.