The Denmark striker has not played for Arsenal for more than two years and appeared certain to leave north London for good this summer.
Wenger said: "I had a chat with him because I blocked his move (to Crystal Palace). I wanted him to stay in the end because I felt that we were short up front, that Yaya Sanogo might need a few months to adapt.
"As well as that Nicklas Bendtner, with the right state of mind and the right focus, has the quality to help the squad to win things.
"He is an honest guy. We want complete commitment and focus from him and he promised that.
"Nicklas Bendtner, with complete focus and commitment, will be a very strong player in our squad."