The deal sees the Catalan club pay an initial transfer fee of 21 million euros, plus a potential 5m euros more in add-ons.
Bayern Munich had emerged as contenders in the market, but Barcelona’s tight relationship with Ajax saw the right-back move to the Camp Nou.
What attracted the Blaugrana to the 19-year-old was his attacking qualities, registering two goals and six assists last season.
Dest arrives to replace Nelson Semedo, who recently departed for Wolves, in Ronald Koeman’s squad.
The teenager, who insisted on joining Barcelona this month, can play either as a right-back or a left-back.
Born to an American father and Dutch mother, Dest earned his first cap for the US national team in 2019.