United are yet to announce the move, two days after Ibra told fans he was signing a day before the club.
The Germans had already lost Ilkay Gundogan to Manchester City and Mats Hummels to Bayern Munich.
They were reluctant to sell Mkhitaryan, 27, but changed their minds after United upped their offer to £26million.
And in a parting dig, Dortmund wished their former player well as he competes in the Europa League.
A statement said: “Borussia Dortmund wish Henrikh Mkhitaryan all the best for the coming season in both the Premier League and in the Uefa Europa League.”
Mourinho has now forked out £56m on players since arriving at Old Traffford, plus Ibrahimovic’s £200,000-a-week wages.
CEO, Hans-Joachim Watzke, added: “”Manchester has made us a tremendous, lucrative offer.
“Had we turned it down, the player would be lost for nothing in 2017. And we have the personnel issue postponed by only one year.”
United play Dortmund on July 22 in Shanghai as part of the International Champions Cup