The 19-year-old will be tied to the Manchester City for the next five years, though he is expected to be loaned to City's sister club Girona in Spain in his first year, reports Xinhua news agency.
According to media reports in Brazil, the City paid 12 million euros ($13.76 million) for the teenager, making the deal the most expensive in Vasco's history.
"We wish [Douglas] the best of luck with the move... and hope that he shines in European football," the Brazilian club said in a statement.
Douglas made 39 first-team appearances for Vasco after being promoted from the club's youth academy last year.
He is the second Brazilian to join Manchester City in less than a year after the arrival of striker Gabriel Jesus from Palmeiras in January.
"We are pleased to welcome Douglas.
He is an exciting player with great potential, and everyone here is looking forward to helping him develop his talent and progress in the game," City's director of football Txiki Begiristain said.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)