Van Nistelrooy replaces Steve Cooper, who was sacked days after the Foxes' 2-1 defeat to Chelsea on Saturday.
The Dutchman has signed a contract to 2027 and will be in the stands for Saturday's clash with Brentford.
His first match in charge will be on Tuesday night when the Foxes host West Ham in the Premier League.
Speaking to Leicester's club website, Van Nistelrooy said: "I'm proud, I'm excited. Everybody that I speak to about Leicester City Football Club is enthusiastic.
"They have great stories about the quality of the people working at the Club, the supporters and, of course, the recent history of the Club is impressive.
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"I'm excited to start and to get to know everyone and give everything I can for the Football Club."
Leicester City chairman, Aiyawatt Srivaddhanaprabha, said: "It is my pleasure to welcome Ruud to Leicester City.
"He joins a Club with a rich history, passionate supporters, and a talented squad, and we are all excited to see the impact he can have as we embark on this new chapter together.
"Ruud's experience, knowledge, and winning mentality will undoubtedly bring great value to us, and we look forward to supporting him in achieving success for our fans and our Club."
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He takes over with the Foxes sitting 16th in the Premier League on 10 points, one point away from the relegation zone.
Leicester's Van Nistelrooy announcement comes on the same week where Jamie Vardy broke the Dutchman's record for the longest consecutive goal-scoring streak in the Premier League nine years ago.
Vardy eclipsed Van Nistelrooy's mark of ten when he smashed home his 11th goal against Manchester United during the Foxes' legendary 2015/16 when they won the Premier League title.
Van Nistelrooy will now get the opportunity to see what makes Vardy tick up close, with the Leicester job marking the third permanent role of his managerial career.
He succeeded Mark van Bommel as PSV Eindhoven's Under-19 team in June 2018 but was promoted to first team manager in March 2022.
The former Manchester United marksman won 33 of his 51 games in charge as he led PSV to the KNVB Cup and Johan Cruyff Shield in the 2022/23 season.
However, he resigned from his post at PSV with one game remaining in the Eredivisie that term due to frustrations regarding a lack of support from above.
Van Nistelrooy made an emotional return to Old Trafford in July as he appointed an assistant coach to Erik ten Hag.
But it failed to be a fruitful partnership as Ten Hag was sacked on October 28 after he oversaw the Red Devils' worst-ever start to a Premier League season.
Van Nistelrooy was subsequently named as United's interim head coach while the club searched and didn't disappoint from his four games in charge.
Ironically, Van Nistelrooy's first game in charge was against Leicester in the EFL Cup as United ran rampant in a 5-2 victory.
Van Nistelrooy followed it up with a 1-1 draw against Chelsea before he oversaw United's first European victory in 13 months as they beat Greek side PAOK 2-0.
In another twist of fate, Van Nistelrooy signed off on his interim stint with a 3-0 win over Leicester in the Premier League.
Unfortunately for Van Nistelrooy, the victory over the Foxes proved to be his final act at United after new boss Ruben Amorim elected not to keep the Dutchman on his new coaching staff.
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"To everyone at Manchester United Football Club, in particular the backroom staff, the players and the fans," Van Nistelrooy wrote on Instagram.
"I want to thank you from the bottom of my heart for your incredible efforts and support. It has been a privilege and honour to represent the club as a player, coach and manager, and I will always cherish the memories we have shared together.
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"M.U.F.C will always have a special place in my heart, and I hope there are many more glory days at Old Trafford very soon - not only because I want the club to do well, but because you all deserve it!
"All the best and take care, Ruud."
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