Man Utd Sign Forward, say BORUSSIA Dortmund
Dortmund chief executive Hans-Joachim Watzke said United's offer has been accepted to avoid the Armenia captain, 27, from running his contract down.
"Had we refused it, the player would be available for free in 2017," Watzke told Dortmund's official website.
United have already made two major signings this summer in defender Eric Bailly and striker Zlatan Ibrahimovic.
Mkhitaryan joined Jurgen Klopp's Dortmund in 2013 from Ukrainian side Shakhtar Donetsk for £23.5m.
He was named Bundesliga Players' Player of the Season in 2015-16 after scoring 18 goals in all competitions, including one against Liverpool - now managed by Klopp - in the Europa League defeat at Anfield.
Mkhitaryan is the son of one of Armenia's most famous footballers, Hamlet Mkhitaryan, and won the first of his 59 caps for his country a week before his 18th birthday.