The 24-year-old Cameroon international will now travel to the Nou Camp to agree personal terms and undergo a medical, Arsenal announced in a statement on their website.
Barcelona confirmed in a statement the fee for Song will be 19million euros (£15million).
The Barcelona statement read: "Barcelona have agreed a deal with Arsenal for the transfer of Alex Song to the Nou Camp. The fee is 19 million euros
"The Cameroon international midfielder will sign for the next five seasons with a release clause of 80 million euros.
"On Monday he'll have a medical and then join the rest of the squad for the official team presentation at the Joan Gamper Trophy."
Barca, who begin their Primera Division campaign against Real Sociedad on Sunday, face Sampdoria in the Joan Gamper Trophy on Monday evening at the Nou Camp.
Arsenal, who saw captain Robin van Persie move to Manchester United on Friday, began their Barclays Premier League campaign with a goalless home draw against Sunderland on Saturday afternoon.
Song sat the match out amid widespread speculation he was on the verge of a move to Barca.
Song, primarily a defensive midfielder, joined the Gunners on loan from French club Bastia in August 2005 before Arsene Wenger made the move permanent at the end of the 2005/06 season.
In the following season he spent the second half of the campaign on loan at Charlton before returning to Arsenal and subsequently establishing himself as a key member of Wenger's squad.
In total, Song has made 204 competitive appearances for Arsenal during his seven seasons at the club, scoring 10 goals.
If he completes his move to Barca, Song would become the Primera Division club's second major signing of the summer after the capture of Spain full-back Jordi Alba from Valencia.
Song would also be following a well-worn path to Barca, with Marc Overmars, Emmanuel Petit, Giovanni van Bronckhorst, Thierry Henry, Alexander Hleb and Cesc Fabregas having all moved from Arsenal to the Nou Camp during Wenger's reign.
Wenger revealed Song had been keen on a move away from Emirates Stadium.
Speaking after Saturday's goalless draw against Sunderland, Wenger said: "He expressed a desire to go to Barcelona.
"It is frustrating, we have learnt to deal with that. I believe as well that the financial potential of some clubs is massive and that makes a difference."
Wenger, however, feels Arsenal have enough cover in midfield.
"We have [Jack] Wilshere coming back, I believe in one and a half months. We have [Abou] Diaby back, we have [Tomas] Rosicky not far away and we might bring another midfielder in as well.
"You have to be patient a little bit [over any new signings]."
Denmark striker Nicklas Bendtner is also expected to leave ahead of the transfer deadline.
However, Wenger played down reports the player was set to move to Italy next week.
"He is likely to move, yes, but there is no deal done at all," Wenger said.