The European champions confirmed the deal, which is expected to be worth between 36 million and 40 million euros, at half-time in their Spanish Supercup clash against Real Madrid.
The deal, which brings to an end a transfer saga that began last year, will take Fabregas back to the club he left as a 16-year-old in 2003.
“We have been clear that we didn’t want Cesc to leave and that remains the case,” said Arsenal manager Arsene Wenger.
“However, we understand Cesc’s desire to move to his home town club and have now accepted an offer from Barcelona. We thank Cesc for his contribution at Arsenal and wish him future success.”
The 24-year-old Fabregas will undergo a medical at Barcelona’s Camp Nou on Monday and, after agreeing personal terms, will be presented to the media.
“We are presenting him on Monday and then we’ll have to see how he is,” said Barcelona coach Josep Guardiola after his side had drawn 2-2 with Real in Sunday’s Supercup.
“We are one more with him in the team in a year when we’ve got the Clubs World Cup and a lot of games. We need more players and we need good players.”
Barcelona president Sandro Rossell was over-joyed at finally sealing a deal for the Spanish international.
“It’s like a son coming home,” said Rossell.
Barcelona had already failed with an offer of 34.4 million euros and an improved reported bid of 29 million euros plus six million euros in future add-ons had also failed to tempt the Gunners.
However, British media reported that Arsenal were finally ready to accept a 36-million-euro offer, with Spanish sports daily Marca putting the deal closer to 40 million euros, of which six million euros would depend on results.
Fabregas spent eight years at Arsenal and made 303 appearances, scoring 57 goals in all competitions.
Named as Arsenal captain in November 2008, he also became a regular in the Spanish national team and has made 58 appearances to date.
Barcelona defenders Carles Puyol and Gerard Pique had already anticipated the deal on Friday when they sent messages on their Twitter accounts welcoming the player before any official announcement.
“Welcome home, happy to have you here @cesc4official,” Puyol tweeted, addressing his message to Cesc’s Twitter account. “@cesc4official, we have got him,” tweeted Pique.
Wenger left Fabregas out of the side which drew 0-0 at Newcastle on Saturday.
He also over-looked Samir Nasri for Saturday’s league opener with the French international widely-expected to seal a move to Manchester City in the coming days.
Wenger, whose Arsenal side begin life without Fabregas on Tuesday in a Champions League play-off against Udinese, will come under intense pressure to spend the money from the deal on new recruits.
But the Frenchman has already ruled out a move for Valencia’s Juan Mata from Valencia, although he has been linked with Shakhtar Donetsk’s Brazilian midfielder Jadson.
Striker Robin van Persie is likely to be the new permanent Arsenal captain.