The transfer brings to a close a long transfer saga dating back beyond last summer, as Dortmund held firm on their £108m asking price to see a deal collapse.
In an agreement confirmed on Thursday, United will pay the fee over five equal installing of just under £15m, with £10m going to Manchester City due to a sell-on clause.
Speaking to reporters on Thursday, Dortmund chief executive Hans-Joachim Watzke said: Were not happy about the money.
Were sad that hes gone.
At the end of the day, it was Jadons exemplary wish to leave, we would have preferred to keep him here.
But he behaved fantastic and gave everything for four years. He made us move forward significantly in the second half of the season.