Vermaelen will sign a five-year deal at Camp Nou after passing a medical on Saturday.
The Primera Division club agreed a deal worth up to £15 million with the Gunners for Vermaelen on Friday, with the Belgium international snubbing interest from Manchester United to make the move to Spain.
The 28-year-old flew to Barcelona on Saturday morning for his medical examination ahead of making the move official.
Given Vermaelen's long struggles with injury, Barcelona insisted on a thorough two-part exam at the Hospital de Barcelona and later at the Clinica de la Creu Blanca.
He came through the tests without any problems, however, and could be unveiled at Camp Nou on Sunday.
Arsenal boss Arsene Wenger had previously stated he would rather Vermaelen move abroad than to another Premier League club, and the defender now becomes the third Gunners captain to join Barca in seven years, after Thierry Henry in 2007 and Cesc Fabregas in 2011.
In a statement on their website, Barcelona hailed Vermaelen's leadership qualities, physical presence and skill on the ball.
It is a skill-set which attracted Manchester United, whose interest in the centre-back first emerged during the World Cup.
New boss Louis van Gaal is on the look-out for ball-playing centre-backs to fit into his 3-5-2 system and had sanctioned a move for Vermaelen, but will now be forced to look elsewhere.
Arsenal could also find themselves short of cover at the back, with new signing Calum Chambers, 19, the only back-up to first-choice pairing Per Mertesacker and Laurent Koscielny.