The 33-year-old’s previous deal was up this summer and he has not played since November, when the latest in a series of calf injuries eventually led to ankle surgery.
Arteta said in April he would not commit to a contract extension until he had proved his fitness, but the deal is now signed.
Wenger told the Arsenal website: “He will stay with us for one more year because he has extended his contract.
“He’s one of the leaders in the club because he’s the captain of the team. I expect him to contribute much more than last season, but he also faces a battle.
“With the number of games we have ahead, we could use his experience, his desire and his quality as it will be vital for next season.”
Arteta’s absence, and injuries elsewhere, contributed to the emergence of Francis Coquelin as a key first-team player in the second half of last season.
Coquelin and Santi Cazorla formed a midfield partnership that helped Arsenal retain the FA Cup at Wembley in May and kept both Jack Wilshere and Aaron Ramsey out of their preferred positions.