The 20-year-old France international signed a five-year contract at the Nou Camp alongside the club’s president Josep Bartomeu.
The News Agency of Nigeria (NAN) reports that the deal is the second most expensive of all time, eclipsed only by Neymar’s recent £200 million move to Paris St-Germain (PSG).
Barca said Dembele’s contract has a release clause of 400m euros (£369.6 million).
While speaking on the move, Dembele said: “I’m very happy to be here. It has always been my dream to be at FC Barcelona and now I’m here I’m very happy.
“It is the best club in the world with the best players in the world.’’
Dembele’s last appearance for Dortmund came in the German Super Cup on Aug. 5.
NAN reports that the Bundesliga side had rejected a bid from Barca earlier in August, with the player on suspension then for missing training.
Dortmund gave an explanation then for rejecting Barca’s approach.
They said this was because their offer “did not correspond to the extraordinary footballing and additional value of the player and the present economic situation of the European transfer market’’..
With regard to the agreed fee, Dortmund said in a statement the payment of add-ons “was agreed up to a maximum total amount of approximately 40 per cent of the fixed transfer fee”.
Barca had had three bids for Liverpool midfielder Philippe Coutinho,rejected with the most recent of which was £114 million.
Officially, the £75 million signing of Luis Suarez from Liverpool in 2014 was their most expensive previous purchase.