The 24-year-old Cameroon international will now travel to the Nou Camp to agree personal terms and undergo a medical.
Barcelona confirmed in a statement the fee for Song will be £15million.
The Barcelona statement read: ‘Barcelona has agreed a deal with Arsenal for the transfer of Alex Song to the Nou Camp. The fee is €19m (£15m).
‘The Cameroon international midfielder will sign for the next five seasons with a release clause of €80m (£63m).
‘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 La Liga 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, began their Barclays Premier League campaign with a goalless home draw against Sunderland on Saturday afternoon.
Wenger revealed Song had been keen on a move away from Emirates Stadium.
Speaking after this afternoon’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.’