It was announced on Monday that an agreement had been reached to take the 21-year-old to Serie A.
He is, however, set to continue his development in Catalunya as he prepares to enter into a five-year deal.
Goal revealed earlier on Tuesday that Barca had made a stunning late move for Malcom as he closed on a switch to Italy.
They have now got their man, with a statement on the club’s official website reading: “FC Barcelona and Girondins de Bordeaux have reached an agreement for the transfer of the player Malcom Filipe Silva de Oliveira. The operation will cost 41 million euros and 1 million in variables.
“The player will sign with the club for the next five seasons, until the end of the 2022-23 season.”
Barca added: “Malcom is an attacking player with a great future ahead of him. He stands out due to his electrifying pace and his technique with the ball at his feet.
“Malcom is a daring, pacey forward with an ability to shoot from distance. Despite being left footed, he is no slouch with his right also and can play on either flank.
“He has mainly operated on the right hand side so far in his career to great success, attacking defenders and getting into the box at every opportunity.
“Aside from his speed, he also has great technical ability and links up well with his team mates, one of the main aspects of Barça’s football.”
Malcom moved to Europe with Bordeaux at the age of 18, having already tasted title success in his native Brazil with Corinthians.
He made 96 appearances for the Ligue 1 club, netting 23 goals.
The highly-rated youngster is the third addition to have been made to the Camp Nou ranks this summer, with Barca having already completed deals for Arthur and Clement Lenglet.