Song, 24, will travel to Spain to agree personal terms and have a medical before finalising the £15 million move.
Last season's La Liga runners up Barca said the player would sign a five-year contract and have a release clause of 80 million euros.
Song will take his medical on Monday and is expected be presented along with the rest of the Barca squad in a friendly against Sampdoria at the Nou Camp later that day.
He is Barca's second major signing of the closed season after they landed Spain full back Jordi Alba from Valencia for 14 million euros.
Arsenal signed Song from French side SC Bastia in August 2005 and made 205 appearances for the Londoners, scoring 10 goals.
Song was not named in Arsenal's squad for their opening Premier League game of the season against Sunderland, which finished 0-0.