The Dutchman will replace Ralf Rangnick, who was installed on a temporary basis after Ole Gunnar Solskjaer was sacked in November.
The Ajax boss will take over from Manchester United’s interim coach Ralf Rangnick in the summer.
Ten Hag said: “It is a great honour to be appointed manager of Manchester United and I am hugely excited by the challenge ahead. I know the history of this great club and the passion of the fans, and I am absolutely determined to develop a team capable of delivering the success they deserve.”
The German took over from Ole Gunnar Solskjaer, who was sacked by the club last November.
Rangnick is expected to step into a two-year consultancy role at Old Trafford.
Football director John Murtough and technical director Darren Fletcher led the search for a new manager, feeding into chief executive Richard Arnold and joint chairman Joel Glazer.
Ten Hag is said to have been interviewed during the March international break and the club has today announced his appointment.
Ten Hag’s compensation is understood to be £1.7m and Manchester United’s good relationship with former player Edwin van der Sar, who is now Ajax’s chief executive, is understood to have played a part in the negotiations.
Other candidates included Julen Lopetegui and Luis Enrique.
Who is Erik ten Hag?
The Ajax boss has risen to become one of the most respected coaches in Europe in the past few years.
He led a young Ajax side to the 2019 Champions League semi-final, beating Juventus and Real Madrid en route.
His side lost to Tottenham in the semi-final after a late goal from Lucas Moura in the second leg.
Ten Hag started his managerial career at Go Ahead Eagles in the Dutch top flight in 2012 before moving to Bayern Munich’s reserve team a year later.
At the time Manchester City manager Pep Guardiola was in charge of Bayern Munich’s first team.
In 2015, he was appointed the sporting director and head coach of FC Utrecht, where he won the manager of the year award in 2016.
Two years later Peter Bosz, the Ajax manager at the time, moved to Borussia Dortmund after losing to Manchester United in the Europa League final.
Ajax initially appointed Marcel Keizer from its youth setup but he was sacked midway through the season and replaced by Ten Hag.
Ten Hag has won two league titles in the Netherlands.
Having worked under Guardiola, Ten Hag is a possession-based manager, who is keen on pressing from the front.
He has also helped develop a number of young players, including Chelsea’s Hakim Ziyech, Manchester United’s Donny van de Beek, Barcelona midfielder Frenkie de Jong, Juventus centre-back Matthijs de Ligt and most recently, Brazilian winger Antony.
The last highly successful Ajax coach to move to England’s top flight – via Inter Milan – was Frank de Boer, who lasted just 77 days at Crystal Palace.-SKY NEWS