It is thought a fee of £35m will be paid for the 24-year-old, who will undergo a medical and discuss personal terms on Monday.
"We have been clear that we didn't want Cesc to leave and that remains the case," said Arsenal manager Arsene Wenger.
"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," he added.
The Spanish international joined the Gunners from Barca's youth academy in 2003 and went on to make over 200 appearances for the club.
The European champions have pursued the midfielder since last summer and it appears the situation is now reaching a conclusion.