The 45-year-old has previously spent time coaching PSV's Under-19s and their reserves, while also gaining further experience working as a first-team assistant coach.
Van Nistelrooy was part of the Netherlands' coaching set-up between 2014 and 2016 and again alongside Frank de Boer at Euro 2020.
He will now take on his first senior managerial role with PSV, whom he represented during a playing career that also saw him star for Manchester United and Real Madrid.
PSV, which announced last month that Schmidt will not be signing a new deal after two full seasons in charge, confirmed the news on its official website on Thursday.
Van Nistelrooy, under contract at Philips Stadion until 2025, said he is fulfilling a life-long ambition of his to manage the 24-time Dutch champions.
"It has always been my dream to be head coach at PSV," he said. "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."
Van Nistelrooy scored 35 goals in 70 games for the Netherlands and 62 goals in the 67 matches for PSV between 1998 and 2001.
He went on to spend five years with United and four years at Madrid, before concluding his playing career with short stints at Hamburg and Malaga.
After embarking on a coaching career in 2014, PSV director John de Jong believes Van Nistelrooy is ready to make the step into senior management.
"All of us, including Marcel Brands, who will be PSV's new general manager this summer, have great confidence in his abilities," De Jong said.
"He is a strong, inspirational leader and his commitment and work ethic will be second to none.
"Van Nistelrooy has gained valuable experience within the PSV organisation but also with the national team and we are highly confident he is ready for his first senior role."
PSV, which is two points behind Ajax with seven Eredivisie games to go, also confirmed it intends to add to Van Nistelrooy's coaching staff in the coming months.