The club said Fabregas, 24, who was not part of Arsenal's squad for their opening Premier League match against Newcastle on Saturday, would have a medical examination on Monday.
Fabregas came through Barcelona's youth academy at the same time as World Player of the Year Lionel Messi before joining the north London club in September 2003.
He became Arsenal's youngest first-team player in the following month when he made his debut against Rotherham United in the League Cup aged 16 years and 177 days.
He also became Arsenal's youngest goalscorer when he netted against Wolves in a 5-1 win that December.
Arsenal have won only one league title (2004) and one FA Cup (2005) since he joined the club, while Barca have claimed three Champions League titles, five Spanish leagues and a King's Cup.
At international level, Fabregas has struggled to hold down a regular starting place in a Spanish team with a rich crop of midfielders, including Barcelona trio Xavi, Andres Iniesta and Sergio Busquets and Real Madrid's Xabi Alonso.
However, he scored the winning penalty in the Euro 2008 quarter-final shootout against Italy, a victory that is seen as a turning point in Spain's international fortunes.
He also played the ball through to Iniesta for his dramatic winning goal in last year's World Cup final.
"We have been clear that we didn't want Cesc to leave and that remains the case," Arsenal manager Arsene Wenger told the club's website.
"However we understand Cesc's desire to move to his home town club and have now accepted an offer from Barcelona. We thank Cesc for his contribution at Arsenal and wish him future success."
