The 24-year-old Cameroon international was left out of the Gunners' squad for their opening Premier League fixture against Sunderland after which the north London club confirmed that they had agreed terms on the deal with the Spanish champions.
Song, who joined Arsenal back in 2005 from French side Bastia, has penned a five-year deal and will provide competition for Sergio Busquets at the base of Barcelona's midfield.
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The midfielder becomes the second high-profile departure from the Emirates Stadium in recent days after Robin van Persie's switch to Manchester United was made official on Friday.
Song made a total of 206 appearances for the Gunners in all competitions, scoring 10 goals in that time.