A club statement said that Barcelona will pay an initial fee of €34m with a potential €7m more in bonuses.
The 28-year-old Turkish international has been a key player in Diego Simeone’s Atletico side in recent seasons after arriving in Spain from Galatasaray in 2011.
And Barcelona said that coach Luis Enrique had requested the signing as the Catalan club look to strengthen their midfield following the departure of long-serving Xavi Hernandez.
However, he arrives at the Camp Nou at a time of uncertainty, with a board running club affairs until elections for a new president are held on July 18.
Barcelona therefore added that the signing comes with a clause that will allow the incoming president to sell Turan back to Atletico, albeit doing so will incur a fine of 10 per cent of the transfer fee paid.
Read more: The National's Transfer Talk page
In any case, Turan will not be able to make his debut for Barcelona until 2016, by which time the reigning European champions will have completed a Fifa-imposed transfer ban.
He is the second new signing made by the Catalan club this close season, after a deal was made with Sevilla last month to sign Aleix Vidal.
Turan became a hugely popular figure with the Atletico fans in his four seasons in the Spanish capital after joining from Turkey.
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.
He 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’s website 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 teammates 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.”
Turan 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.
Follow us on Twitter @NatSportUAE