The 24-year-old Armenia forward will sign a deal in the next few days following successful talks between the BVB and Shakhtar
Mkhitaryan, 24, will complete a switch to Dortmund later this week for €27.5 million and will sign a four-year deal with the Bundesliga runners-up.
The Armenia forward, who also plays in midfield, completed his medical with BVB on Monday and although a contract is yet to be signed, the stock market has been alerted.
A statement on the German club's official website read: "Borussia Dortmund AG and FC Shakhtar Donetsk have agreed on the transfer of the Armenian international Henrikh Mkhitaryan, born on 21 January 1989, to Borussia Dortmund.
"Borussia Dortmund and the player have reached a general agreement about the financial conditions of a contract running until 30 June 2017. Details are yet to be agreed upon."
Mkhitaryan joins Pierre-Emerick Aubameyang and Sokratis Papastathopoulos from Saint-Etienne and Werder Bremen, respectively, as Dortmund's latest recruits since losing Mario Gotze to Bayern Munich.
Mkhitaryan, who was also wanted by Liverpool this summer, scored 44 goals in 106 matches for Shakhtar.