The Belgium international centre-back completed his switch to the Liga giants from Arsenal on Sunday, with Barcelona confirming a €10 million fee was paid with up to €5 million due depending on his own personal performances, while a possible €3.8 million could be due from Barca's achievements.
Vermaelen had been heavily linked with a switch to Old Trafford throughout the close-season, with new United manager Louis van Gaal reportedly keen to bolster his defensive options.
However, the 28-year-old revealed there was only one option once he heard of Barca's interest.
"Coming to Barca is a dream come true," he said at a press conference. "It wasn't a difficult decision at all.
"I'm very happy to be here, for a lot of players it's a dream to play for this big club. It's always a big challenge but I look forward to it.
"I will be playing with the best players in the world, training with them every day and I hope to get better as a player.
"You know when you come to a club like this they have world-class defenders. There's competition, I'm excited, it's down to me to show I can play for this club."
Vermaelen joined Arsenal in June 2009 and had been club captain at the Emirates Stadium.
However, he suffered problems with form and injuries and lost his position to regular centre-back pairing Per Mertesacker and Laurent Koscielny last term.
Vermaelen was quizzed on his previous injury issues, but the former Ajax man is confident his fitness concerns are a thing of the past.
"Last year was a bit disappointing with injuries," he added. "It happens sometimes in a career with a player. I hope to come here and hope that I can be strong here and play all the games.
"I'm confident with the medical team here I can be fit and play a lot of games."
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