United announced on Monday that an agreement had been reached with Rangnick over a relationship that is set to span two and a half years, with him initially taking charge until the end of the season before moving into a consultancy role.
The 63-year-old's start at the club was delayed due to work permit issues, but the club confirmed his paperwork was approved on Friday (AEDT) and he will take charge of his first game on Monday (AEDT) when United hosts Crystal Palace.
Michael Carrick took charge of Friday's (AEDT) 3-2 win against Arsenal, before the former England midfielder stepped down from his role with the club.
Speaking at his first United media conference on Friday, Rangnick told reporters why he had taken the job, having turned down a similar offer from Chelsea last year after the dismissal of Frank Lampard at Stamford Bridge.
"At the time when Chelsea contacted me in February, we only spoke about the option to be interim manager for four months without any perspective to work in the long term together," the German said.
"Here, we're talking six and a half months, so we only have one third of the games played in the [Premier League], and as you know, we've also agreed on a two-year advisory role.
"If a club like Manchester United contacts you for such a role, you cannot possibly turn it down."
The former RB Leipzig boss confirmed he has studied his new side's latest games, including recent chastening defeats to Liverpool, Manchester City and Watford, which ultimately led to the dismissal of Ole Gunnar Solskjaer.
"Obviously I've watched the latest games," he added. "Not only last night but also against Watford and Chelsea on TV when I didn't know there would be contact in the next days. I also watched with interest the games against Liverpool and Manchester City.
"I'm pretty well acquainted with what's happening at the club and in the [Premier League]. It's obvious the team have abundant talent, young talented players but also experience in the squad. The major target for me is to bring more balance into the team."
United has conceded 24 goals in its 14 league games, with only four teams having shipped more, which Rangnick has noted.
He added: "Even yesterday, we conceded two goals and we needed three in the end to win the game. If you look at the total number of goals conceded, it's nearly two on average per game. This is just too much.
"This is my approach to help the team to get more balance and more control of the game. Yesterday's game was exciting for the fans but for myself, as the future coach, those are not the kind of games that you need every day.
"This is my approach, and I'll try to help these outstanding, talented players to try and keep away from their own goal."
United sits seventh in the Premier League after Friday's (AEDT) win, 10 points behind Liverpool in third, and Rangnick is under no illusion of the size of the task at hand to try and close that gap.
"The aim in the first instance is to win the first game," he continued. "It will not be easy [to implement ideas] in the middle of the season. The difference between us and the top three is big. It's about developing the performance, getting a feeling of how we can control the game."