The 24-year-old Armenia forward will sign a deal in the next few days following successful talks between the two clubs and the player.
Mkhitaryan, 24, will complete a switch to Dortmund later this week with reports suggesting the deal is around 25 million euros and will sign a four-year deal with the Bundesliga runner-up.
The Armenia forward has had his medical with BVB on Monday and although a contract still has not been signed, the stock market has been alerted.
A statement on the club's official website read: "The Borussia Dortmund AG and FC Shaktar Donetsk have agreed on the transfer of the Armenian international Henrikh Mkhitaryan, born on the 21st of January 1989, to Borussia Dortmund.
"Borussia Dortmund and the player have reached a general agreement about the financial conditions of a contract running until the 30th of June 2017. Details are yet to be agreed upon."
Mkhitaryan joins attacker 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 scored 44 goals in 106 matches for Shakhtar.