The Turkish international joined Barcelona earlier this week for £24 million however, he cannot play for the club until 2016 due to a transfer embargo on the Catalan giants.
Turan has signed a five-year deal with the UEFA Champions League winners keeping him at the Camp Nou until July 2020.
“Everyone comes from somewhere and I come from a small place in Turkey to go and play for the best team in the world,” Arda told Sport.
“Playing at Barca is a dream, every footballer wants to play at the Camp Nou, the best stadium I’ve been at.
“Not playing until January is a problem, but I’m not here for six months. I’m here to win trophies over five years.”
Barcelona are currently preparing for new presidential elections on 18 July. Bartomeu, Joan Laporta, Toni Freixa, Agusti Benedito and Joan Batiste are the candidates hoping to take charge at the club.
Turan could end up being returned to Atleti for an effective cost of 3.4 million euros if Bartomeu loses the election.
The 28-year-old winger provided six assists and three goals in 46 appearances in all competitions for Atletico Madrid last season.