The former RB Leipzig boss will replace Ole Gunnar Solskjaer for the remainder of the 2021-22 season after leaving his role as Head of Sports and Development at Lokomotiv Moscow.
Rangnick is set to move into a two-year consultancy role at Old Trafford following his stint in the dugout and is expected to have a say in the appointment of a new permanent head coach next summer.
"He was our number one candidate for interim manager, reflecting the invaluable leadership and technical skills he will bring from almost four decades of experience in management and coaching.
"Everyone at the club is looking forward to working with him during the season ahead, and then for a further two years in his advisory role."
Rangnick added: "I am excited to be joining Manchester United and focused on making this a successful season for the club. The squad is full of talent and has a great balance of youth and experience.
"All my efforts for the next six months will be on helping these players fulfil their potential, both individually and, most importantly, as a team. Beyond that, I look forward to supporting the club's longer-term goals on a consultancy basis."
Michael Carrick is set to remain in charge until Rangnick's work permit is sorted, so it remains unclear if the German will be on the touchline for Thursday's Premier League encounter with Arsenal. body check tags ::