Barca will pay 34 million euros ($37.6 million) for Arda, plus another seven million in variables, and the 28-year-old's contract will be for five years, the club said on their website (www.fcbarcelona.es).
As things stand, however, he will not be able to play until January as Barca have been banned by FIFA from registering new signings until then, after they broke rules on the transfer of foreign under-18 players.
The deal to sign Arda was also complicated by the fact that the club are in the midst of a presidential election campaign and are being administered by a special commission, which had to approve the transfer.
The commission included an unusual clause which means whoever wins the July 18 election has the option within two days of selling Arda back to Atletico less 10 percent of the fixed fee of 34 million euros.
Arda became a hugely popular figure with the Atletico fans in his four seasons in the Spanish capital after joining from Galatasaray.
With his ability to unlock stubborn defences with a killer pass, the stocky and heavily-bearded midfielder was a key figure in Atletico's charge to a first La Liga title in 18 years and their run to the Champions League final in 2013-14.
Arda made his debut for Turkey in 2006 and helped Fatih Terim's side reached the semi-finals of Euro 2008, where they lost 3-2 to Germany.
He spoke about his role on the pitch in an interview published on FIFA.com in October.
"I take care of organising the attack," he said.
"When we’re under the cosh, I can hold up the ball to give my team mates a breather, maybe forcing someone into fouling me.
"Before kickoff my heart rate is off the scale but once the whistle blows, I’m completely calm.
"On the pitch I’m at ease, though I’m not sure why that happens. I’m probably a bit crazy."
Arda may struggle to get a regular starting spot in a Barca midfield which also features Andres Iniesta, Ivan Rakitic and Sergio Busquets but would be a useful player to bring off the bench in the second half.
($1 = 0.9050 euros)
(Editing by Clare Lovell)
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