The 22-year-old will replace Victor Valdes between the posts at Camp Nou next season and reveals that there were a number of other clubs interested in his services
The Germany international completed his move to Barca on Monday, having previously been at Bundesliga club Borussia Monchengladbach.
There were fears that his switch may not go ahead when the club were handed a two-window transfer ban in April but that sanction has since been put on hold subject to an appeal.
The 22-year-old was unveiled at Camp Nou on Thursday and, despite joining at the end of a rare season in which Barca failed to win a trophy, Ter Stegen is confident he made the right decision.
"Barca is the start of a new stage in my career and I'm very proud to be able to join the system," he told the press after signing a five-year deal. "That's easy to say but there's a lot of substance to it. I'm very happy with the confidence they have put into me.
"From the beginning, I knew that coming to this club would be something special. There were other clubs but I don't think this is the time or place to speak about them.
"This was always my No.1 option. There couldn't be anywhere better to be than Barca. There aren't many teams who have got so many good players with so much personality."
Ter Stegen is expected to be the first-choice keeper for newly appointed coach Luis Enrique following the departures of Victor Valdes and Jose Manuel Pinto.
The long-serving Valdes was due to leave at the end of the season anyway but saw his campaign curtailed by a knee injury and the German paid tribute to the his predecessor.
"Victor Valdes is an extraordinary goalkeeper who has done so much for this club. He's performed so well for so many years and won so many titles," he added, "but he's not here anymore and I am. I know what my job is - Barca have chosen me and I'm very proud of that.
"This is a big challenge - defending the Barca goal is one of the greatest things I could hope for in life. Evidently, I want to be the best I can and I think playing with these players is something I can adapt to. I have to continue with my own style and adapt that to Barca's way of playing."