The 24-year-old Cameroon international midfielder has signed a five-year contract at the Nou Camp after the clubs agreed a £15m deal.
Song, whose contract will contain a release clause of 80m euros (£63m), passed a medical on Monday.
“I’m very happy to be here, this is the best team in the world. Playing at a club like Barca is something I wanted when I was young,” Song told Barca TV.
“I hope the team will continue to win, this is a winning team. They win everything.”
Arsenal are close to signing 23-year-old Turkey international midfielder Nuri Sahin on a season-long loan deal from Real Madrid as a replacement.
Song did not play in Saturday’s 0-0 draw with Sunderland, after which Arsenal confirmed an agreement had been reached with Barca.
The Spaniards will present him to the media on 11:00 BST on Tuesday.
“It’s always frustrating losing good players, but we have plenty of players in midfield,” said Gunners boss Arsene Wenger.
“We are looking to bring one more midfielder in, and maybe one defender as well because we still feel we are short in some positions.”
Sahin joined Real Madrid from Bundesliga champions Borussia Dortmund last summer but struggled to make an impact, and head coach Jose Mourinho has said he is free to find a new club.
Song, who had two years left on his contract, joined Arsenal as a 17-year-old from French side Bastia in 2005.
He initially arrived on a one-year loan deal, with a £2.75m fee agreed to make the move permanent.
Song went on to make more than 200 appearances for Arsenal, including 34 in the Premier League last season.
The midfielder will now link-up with former team-mate Cesc Fabregas at Barcelona who he believes will help him settle in at the Nou Camp.
“I know Cesc very well,” Song added. “He’s a very good friend of mine, he will help me to integrate.”
With Abou Diaby, Jack Wilshere and Tomas Rosicky returning to match fitness, Wenger says he is happy with his midfield options.
Arsenal have signed striker Olivier Giroud, forward Lukas Podolskiand midfielder Santi Cazorla, but captain Robin van Persie - who scored 30 league goals last season – has joined Manchester United. (According To The BBC)