The 18-year-old has completed a medical in Spain and signed a five-year contract that includes a release clause of €25 million.
McGuane’s deal will keep him in Catalonia for three seasons, plus two option years.
The midfielder, who had been at Arsenal since the age of six, made his first two senior appearances under manager Arsene Wenger in Europa League group-stage matches against BATE and Red Star Belgrade this season.
McGuane, an England youth international, will join Barca's B team with a view to earning a spot in the first-team squad in future.
"We would like to thank Marcus for his contribution and wish him well at Barcelona," Arsenal said in a statement.
"The transfer is subject to the completion of regulatory processes."