Rene Hake was also hired in an assistant role to complete an all-Dutch managerial team.
Ten Hag has signed a contract extension that will keep him at the Premier League club until 2026 despite a poor season in which United finished eighth in the standings.
"Now is a good time to refresh the coaching team as we look to build on the achievements of the past two years and push to the next level," Ten Hag said in a statement.
Van Nistelrooy scored 95 goals in 150 Premier League appearances for United between 2001 and 2006 and is the team's top Champions League scorer with 35 goals. He netted 35 goals in 70 appearances for the Netherlands.
Van Nistelrooy guided PSV Eindhoven to a second-place finish in the Eredivisie and a Dutch Cup triumph in 2022/23.
"Together with Erik, we are working to strengthen all areas of our men's first-team operations, and refreshing the coaching staff is an important part of that," United's sporting director Dan Ashworth said.
"It's a particular pleasure to welcome Ruud back to the club where he enjoyed so much success as a player, and I know that he and Rene will help reinforce the winning mentality and high standards we are aiming for."
Hake has coached a number of teams in the Netherlands for the past 20 years. Mitchell van der Gaag and Benni McCarthy have both left the Old Trafford coaching staff.
United's Dutch midfielder Donny van de Beek has completed a permanent move to Spanish Liga club Girona.
