In addition to the €21m base fee, Ajax will receive €5m in variables for the 19-year-old.
Dest, who chose Barcelona over Bayern Munich, has signed a five-year deal with a €400m release clause.
— FC Barcelona (@FCBarcelona_es) October 1, 2020
The Catalan club will present Dest on Friday afternoon and he is the first signing of the Ronald Koeman era.
Dest leaves Ajax after rising through their youth system and making 38 first-team appearances.
Although born in the Netherlands, the attacking full-back opted to represent the USA at national team level.
He made his USMNT debut against Mexico in 2019 and has since made two further appearances against Uruguay and Cuba.