Barcelona has put a sizeable chunk of its Neymar money to use after losing the Brazilian to Paris Saint-German for a record $A331 million fee.
Dembele will wear the number 11 jersey vacated by Neymar after signing a five-year contract with a reported $A601 million release clause.
The unsettled Dortmund star was suspended earlier this month for missing training as he tried to finalise a move to Camp Nou.
The 20 year-old joined BVB last year from Rennes for $A22.5 million and made an immediate impact, scoring 10 times in 49 matches across all competitions and providing 20 assists.
He was named in the Bundesliga team of the season and scooped the man-of-the-match award after opening the scoring in Dortmund's 2-1 DFB-Pokal final triumph over Eintracht Frankfurt.