Louis Van Gaal has signed a three-year contract and Ryan Giggs will remain as assistant manager.
The former Ajax, Barcelona and Bayern Munich coach has proven to be one of the most successful coaches in European football.
"It was always a wish for me to work in the Premier League. To work as a manager for Manchester United, the biggest club in the world makes me very proud," he said.
"This club have big ambitions. I too have big ambitions. Together I'm sure we will make history."