United have not yet confirmed the transfer, but Dortmund chief executive, Hans-Joachim Watzke, said in a statement: "Manchester made us an enormously lucrative offer Had we rejected it the player would have left in 2017 without a fee and we would have just delayed the issue for a year."
Mkhitaryan made his professional debut for FC Pyunik in his home country in 2006 at the age of 17 and moved to Ukrainian side Metalurg Donetsk in 2009 before switching to Shakhtar Donetsk the following season.
His success as a goalscoring midfielder earned him a move to the Bundesliga in July 2013, Dortmund paying a then club record 27.5 million euros ($30.6 million) for his services.
Last season Mkhitaryan was instrumental in helping Dortmund return to the Champions League and his good form helped carry them to second in the Bundesliga and to the German Cup final.
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Calm and composed under pressure, Mkhitaryan is capable of breaking open even the tightest defence with his passing skills and reading of the game.
He scored 11 goals and set up another 15 in the Bundesliga last season, but had been hinting at a move for several months.
Dortmund have also recently sold defender Mats Hummels to Bayern Munich and midfielder Ilkay Guendogan to Manchester City.
($1 = 0.8978 euros)
(Reporting by Neville Dalton, additional reporting by Karolos Grohmann, editing by Ed Osmond)
