Financial terms of the deal were not disclosed, but Italian media said Roma will pay around 37 million euros (£33m) for the 21-year-old.
He is, however, set to continue his development in Catalunya as he prepares to enter into a five-year deal.
Malcom had been a reported target for several European clubs, including Premier League sides Arsenal and Tottenham Hotspur, but English clubs may have been put off from making a bid as he needed a United Kingdom work permit to play in the Premier League.
Roma supporters had even gathered at the airport in Italy's capital city to greet Malcom on Monday night, but he never arrived.
Barcelona have now confirmed that they have won the race to sign the player for a fee of €42m (£37.34m) - subject to a medical - with Malcom committing his future to the Catalan giants until 2023.
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Roma have now been informed that he wishes to join Barca.
Barca face Tottenham in Los Angeles on Saturday in the International Champions Cup, when Malcom could make his debut for his new club.
Malcom scored 12 goals in 35 Ligue 1 appearances for Bordeaux last season and has made 96 appearances in all competitions since joining from Corinthians in January 2016.
Borussia Dortmund and several Premier League teams were linked, but it was Roma's sporting director Monchi who looked to have sealed a deal to sign the talented attacker.