The Denmark striker has not played for Arsenal for more than two years and appeared certain to leave north London for good this summer.
But a move to Crystal Palace was scuppered by Wenger at the last minute when his loan deal for Demba Ba fell through, and Bendtner now faces a battle to regain fitness and provide cover for Olivier Giroud.
Only Theo Walcott of the current squad has more Arsenal goals than Bendtner's 45, and Wenger is convinced the 25-year-old can play an important role in this season's chase for a first trophy since 2005.
He said: "I had a chat with him because I blocked his move. 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."