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 Barca were handed a two-window transfer ban in April for breaching rules over the signing of international players under the age of 18, but that sanction has since been put on hold.
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 that he made the right decision after having the chance to discuss moves elsewhere.
"Barca is the start of a new stage in my career and I'm very proud to be able to join the system," he said after agreeing a five-year deal.
"That's easy to say but there's a lot of substance to it. I'm very happy with the confident 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 number one option. There couldn't be anywhere better to be than Barca.
"There was never a second option, Barca was always first.
"There aren't many teams who have got so many good players with so much personality."
Ter Stegen will likely be used as number one for recently appointed Barca boss Luis Enrique following the departures of Victor Valdes and Jose Manuel Pinto.
Long-serving goalkeeper Valdes was due to leave at the end of the season anyway but saw his campaign curtailed by a knee injury, and Ter Stegen paid tribute to the 32-year-old.
He also stated his intention to stamp his authority on the goalkeeping position at the club.
"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."
