Barca did not publish any financial details but Spanish media said they had agreed to pay about 19 million euros ($25.5 million) to secure his services.
The 28-year-old defender is the second Belgian player to play for the Catalan club after Fernand Goyvaerts (1961-1965) and his purchase follows the acquisition of another centre back, Frenchman Jeremy Mathieu, who joined last month from Valencia.
Barca's defence was a weak point last season, when they failed to win major silverware for the first time in six years, and coach Gerardo Martino was replaced by former Barcelona and Spain midfielder Luis Enrique.
Vermaelen, who has passed a medical and will be presented at the Nou Camp stadium and sign his contract on Sunday, moved to Arsenal in 2009 after a nine-year stint at Ajax Amsterdam who he joined from Belgian side Germinal Beerschot.
He quickly became a favourite in the dressing room and amongst the fans while also being promoted to club captain.
Vermaelen's career has been hampered by injury, however, and he featured only 21 times in the 2013-14 season after falling behind Laurent Koscielny and Per Mertesacker in the pecking order.
He played a total of 150 games for Arsenal in all competitions, scoring 15 goals, and will compete for a place in the Barca back line with Spain international Gerard Pique, Mathieu and the club's academy graduate Marc Bartra. Javier Mascherano has mostly played in central defence since joining Barcelona from Liverpool in 2010 but after his excellent performances in midfield for Argentina at the World Cup he is widely expected to feature there for the club next term.
On their website (www.fcbarcelona.es) Barca described Vermaelen, who has captained Belgium and has 47 caps, as "a central defender who can take the ball out of defence, is tactically very good, and is a strong tackler.
"As well as his defensive presence, he is also known for possessing great vision," they added.
"This is why the Belgian international can not only play at the centre of the defence but also has the natural ability to play at left back." Barca start their La Liga campaign, when they will chase a fifth title in seven years, at home to Elche on Aug. 24.
($1 = 0.7458 Euros)
(Reporting by Iain Rogers, editing by Ken Ferris)
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