Malcom had been expected to join Roma, but Barça's failure to convince Chelsea to sell Willian saw them hijack the proposed deal and steal the talented 21-year-old from under the nose of their 2017/18 Champions League conquerors.
"This is a boyhood dream come true," Malcom told Barça's official website.
"I hope to bring a lot of joy to the fans. I can't wait to get started. I'm here to help my team-mates with my style," he added.
"It is a unique feeling. I'm realising a dream and I'm going to play for the best club in the world.
"I always try to help my teammates and I am looking forward to meet the ones I will have at Barcelona. It is important to know the people you are going to play with."
Malcom, who is expected to be handed the vacant number seven shirt last worn at Camp Nou by Arda Turan, will complement an already strong unit of Barça attackers featuring Lionel Messi, Luis Suarez, Ousmane Dembele and Philippe Coutinho.
Malcom first arrived in Europe in 2016 when he joined Bordeaux from Brazilian club Corithians. He earlier had made his debut in the Brasileiro in 2014 shortly after his 17th birthday.
Last season, he scored 12 Ligue 1 goals for Bordeaux, only one fewer than Kylian Mbappe managed for Paris Saint-Germain, while he also provided a further seven assists.