Dest is the latest young American to make the jump to a top European club. His deal with Barcelona follows international teammate Weston McKennie's move to Juventus in August, Gio Reyna's debut with Borussia Dortmund, and Tyler Adams' transfer to RB Leipzig.
Barcelona set Dest's buyout clause at a virtually untouchable €400 million.
The 19-year-old will sign a five-year contract with the Blaugrana before he's presented to the media Friday.
Bayern Munich were reportedly involved in negotiations for the right-back but ultimately lost out.
Dest, born to a Dutch mother and Surinamese-American father, joined Ajax as a 12-year-old and made his first-team debut in July 2019. He made 36 appearances in all competitions in his first and only full season with the senior side.
Dest chose to represent the United States in international competition after gaining experience with the Stars and Stripes at the under-17 and under-20 levels.
Ronald Koeman, Barcelona's newly appointed manager, tried to convince Dest to choose the Netherlands while he was the coach of the national team. Though unsuccessful then, Koeman will now have the chance to manage the youngster at Barca.