Vermaelen sustained an Achilles injury in 2010 followed by a series of niggling problems and featured only 21 times for Arsenal in the 2013-14 season after falling behind Laurent Koscielny and Per Mertesacker in the pecking order.
The 28-year-old signed his five-year Barca contract and was presented to fans at the Nou Camp on Sunday before setting out his ambitions at the Spanish club, where he will compete for a starting place with the likes of Gerard Pique, Jeremy Mathieu and Marc Bartra.
"When you come to a club as big as Barca you have to prove your worth and playing time is not a given," Vermaelen told a news conference.
"Barca's centre backs are very good, there is competition but it's up to me to show I can play here," he added.
"I want to put the injuries behind me and look forward. Last season was tough but I want to start again from scratch and I am sure I will have a fantastic season.
"I have a lot of desire to play and I am aware that expectations are very high."
Barca's defence was a weak point last season, when they failed to win major silverware for the first time in six years.
Gerardo Martino has been replaced as coach by former Barca and Spain midfielder Luis Enrique and as well as strengthening the defence with Vermaelen and Mathieu the club have bought in Uruguay striker Luis Suarez, Croatia midfielder Ivan Rakitic and goalkeepers Marc-Andre ter Stegen and Claudio Bravo.
Vermaelen sustained a minor hamstring injury at the World Cup finals in Brazil in June and said he still needed a few weeks to get back to full fitness.
Barca start their La Liga campaign, when they will chase a fifth title in seven years, at home to Elche on Aug. 24.
Jordi Mestre, a Barca vice president, told reporters the club had agreed to pay as much as £15 million for Vermaelen, including a fixed fee of £8m, depending on his performances and the team's results.
- Sports & Recreation
- Jeremy Mathieu
- Gerard Pique
- Laurent Koscielny