The 37-year-old has made 21 appearances since returning from retirement in January and been integral as United battled for their 20th league title before losing out to rivals Manchester City on goal difference.
"It's been done. He's staying. I am delighted," Sir Alex confirmed at the club's Player of the Year awards dinner on Monday night.
"He knew he had made a mistake. He now realises if he plays 25 or 30 games next season, they will be of real quality.
"I think this will be Paul's last season. We know him very well. We have had him since he was a kid. We know how to use him."The Red Devils boss also confirmed his intention to bring in new signings, as they look to reclaim the title from local rival Manchester City next season.
"Yes we want to add to the squad that's in process at the moment. We have set our stall on certain players," he confirmed."