After impressing while at Borussia Monchengladbach, the German was unveiled as Victor Valdes's successor at Camp Nou on Thursday and he hopes for a long stay there
The Germany international's long-awaited move to the Catalan club was confirmed in May as they look to replace Victor Valdes, who is set to leave this summer.
"I'm fulfilling my dream," he told Kicker.
"This is the right move for me. If all goes well, I can play for many years at Barcelona. Of course you have a certain respect for this new phase of life.
"I certainly wouldn't have decided to go before."
Ter Stegen's immediate aim is to settle into life at Camp Nou, having spent his entire career to date with hometown club Borussia Monchengladbach.
"For me, the important thing now is settling at Barcelona," he remarked. "I'm happy to have new team-mates and learn a new language."
The 22-year-old was not included in Germany coach's Joachim Low's 30-man preliminary squad for this summer's World Cup.