Song, 24, will travel to Spain to agree personal terms and have a medical before finalising the move, Arsenal said on their website.
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, the Catalan side said.
He is expected to provide cover in the centre of defence, a priority new coach Tito Vilanova laid out when he stepped up from assistant to replace Pep Guardiola last season.
Barca have struggled at the back recently with ageing captain Carles Puyol, who is 34, struggling with a string of injuries, and Eric Abidal out as he recovers from a liver transplant.
Sergio Busquets and Javier Mascherano have dropped back from midfield to play alongside Gerard Pique at the back, and Song will provide further options to fulfil a similar role.
He is Barca's second major signing of the close 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.
