Van Nistelrooy will take over from current boss Roger Schmidt, who will leave this summer, and has agreed a three-year contract.
The 45-year-old had a spell with PSV as a player, winning two Eredivisie titles before further stints at Manchester United, Real Madrid, Hamburg and Malaga.
Van Nistelrooy has been working as an assistant with the Dutch national team since his retirement in 2012 and the youth sides of PSV.
"PSV has appointed 45-year-old former striker Ruud van Nistelrooy as their new manager on a 2025 contract to replace Roger Schmidt, who will leave his post at the end of the season when his contract ends," PSV explained in a statement published on the club's official website.
Van Nistelrooy said: “It has always been my dream to be head coach at PSV.
“I’ve worked intensively with Toon Gerbrands, PSV’s current General Manager, the past few seasons.
"I was convinced I could pursue a professional coaching career and originally thought I needed one more year to gain experience.
"But sometimes things do go their way and you find out that life is not completely manageable. This is the right moment to take the next step.”
"The appointment of Marcel Brands as PSV's general manager and the conversation we've had were the final push I needed to make a conscious choice and take this step.
"PSV are ready to embark on a new path this summer and I am ready to play my part.
"Talks with the board of directors have reinforced the idea that we are ambitious and look to create something special in the long term. I am excited for the task in hand at PSV."
PSV are currently second on the Eredivisie table, two points behind leaders Ajax Amsterdam.
