The Cameroon midfielder has signed a five-year contract, with the Gunners receiving a £15 million fee.
Song – who was left out of the squad for Saturday's goalless draw with Sunderland at the Emirates Stadium – joins former Arsenal team-mate Cesc Fabregas at the Spanish giants.
Barca club doctor Ricard Pruna told the club's official website: "He has a very low fat percentage and very good quality muscle. I don't think he has had any muscle injuries since he was 17. This is good news. All tests have gone well and he is available for the coach (Tito Vilanova)."
Song registered more assists in the Premier League than any other Arsenal player last season, with 11 to his name. Arsenal have therefore lost their most creative player this summer as well as their top scorer following Robin van Persie's move to Manchester United.
Arsenal manager Arsene Wenger said in his regular open letter to the club's supporters: "As you know the club agreed terms to sell Alex Song to Barcelona. We did this because we have Jack Wilshere coming back, we have Abou Diaby back, we have Tomas Rosicky not far away and we will try to bring in another midfielder as well."
Barca, who finished second in La Liga last season, got their new campaign off to a winning start at the weekend with a 5-1 home win over Real Sociedad.
The victory featured a competitive debut for Spain left-back Jordi Alba and David Villa coming off the bench to score on his first appearance since breaking his leg back in December.