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."
Arsenal, who on Friday saw captain Robin van Persie move to Manchester United, began their Premier League campaign with a goalless home draw against Sunderland this 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 fullback 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.