The €222m received from Paris Saint-Germain for Neymar sparked the Liga side's pursuit of Dembele and Liverpool's Philippe Coutinho in the close season, but they saw bids for each rejected.
While Liverpool have stood firm on their insistence that Coutinho is not for sale, Dortmund have surrendered to Dembele's wishes and allowed him to leave.
He will arrive in Spain over the weekend to undergo a medical and sign his contract ahead of his official unveiling at Camp Nou on Monday.
He is the fifth signing Barca have made in the current window, joining Marlon, Nelson Semedo Paulinho and Gerard Deulofeu in moving to Camp Nou.
