"I'm proud to be the first-ever American here," he told a news conference. "It's a dream come true and I can't wait to get started with my new teammates.
"Bayern are a great club and there was interest from them, but I followed what my heart told me to and for that I signed for Barca.
"I think it was the right decision. They are a club with so much history and I've always wanted to play here."
Dest came through the youth ranks at Ajax, making 23 league appearances, and attracted interest from a number of clubs across Europe.
His arrival means he will play under coach Ronald Koeman, who unsuccessfully attempted to convince the 19-year-old to represent Netherlands at international level while in his previous job.
"[Playing under] Koeman of course was an influence, because he's Dutch and it will be easier to communicate with him," he added.
Dest also said he is happy to play alongside Lionel Messi and cited former Barca full-back Dani Alves as a player he wants to emulate at the club.
"It's amazing to play with the best player in the world, I looked up to him [Messi]," he added. "I will run as much as I have to. I will run for everybody in the team.
"If I see him today, in the afternoon, it will be so exciting to meet the best player in the world.
"I think right-back or left-back, those are my best positions. I will keep it like that. I will try and be like Dani Alves, he's my role model, so I want to run forward and run backward all the time. If I have to do more training for that, I will."
Dest could make his debut in Sunday's La Liga clash at home to Sevilla.
Information from Reuters was also included in this report.