The club said that they had a number one candidate for interim manager.
The interim manager of Manchester United is subject to work visa requirements.
The 63-year-old takes over from Ole Gunnar Solskjaer, who was sacked on November 21.
The head of sports and development at Lokomotiv Moscow has left to take the job.
"I am excited to be joining Manchester United and focused on making this a successful season," said Rangnick.
After the end of the season, Rangnick will stay on at Old Trafford for two more years in a consulting role.
If his work permit application is received in time, he could be in charge of United for the first time against the Gunners on 2 December.
Michael Carrick will remain in charge of the side if not.
The squad is full of talent and has a good balance of youth and experience.
All my efforts for the next six months will be on helping these players fulfill their potential, both individually and as a team.
I will be supporting the club's goals on a consulting basis.
Both Thomas Tuchel and Juergen Klopp have heaped praise on their colleague, who has built an impressive coaching reputation during his time in Germany.
He took Ulm to the first step to promotion to the Bundesliga before taking charge of other teams.
He won the German Cup with Schalke in 2011.
He was in charge of the team that lost to United in the semi-finals of the European Championship in the 2010-11 season.
John Murtough, United's football director, said that Rab is one of the most respected coaches in European football.
He was our number one candidate for interim manager and he will bring a wealth of experience in management and coaching to the position.
"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."
More to come.
