Dest, 19, joins Barca on a five-year deal, with Ajax receiving a fee of around €21 million plus a potential €5m in add-ons. A buyout clause is set at €400m.
Dest, who will wear the No. 2 shirt, was also on Bayern Munich's radar and, according to ESPN sources, the European champions twice travelled to Amsterdam for talks although no deal could be agreed.
𝐈𝐍 𝐃𝐄𝐒𝐓 🇺🇸 𝐖𝐄 𝐓𝐑𝐔𝐒𝐓 pic.twitter.com/mgSFWcqjwQ— FC Barcelona (@FCBarcelona) October 1, 2020
Sources also told ESPN that Barcelona boss Ronald Koeman was key in agreeing to a transfer for the defender thanks to his long-standing interest.
Dest arrives after spending almost a decade with Ajax, where he came through the youth ranks.
It has been a remarkable rise for the defender, and while he is expected to play a starting role at Barca, sources have told ESPN the club have called for patience.
Barcelona see him as a player with all the attributes necessary to succeed at the Camp Nou, but they believe he is still developing as a player.
Dest enjoyed a breakthrough season in 2019-20 and went from the fringes of the senior squad to being one of the most sought-after full-backs in Europe. He signed his first professional contract with Ajax in December 2018 and made his first-team debut in August 2019.
After just one season in Ajax's first team, Dest joins Barcelona, where he will battle Sergi Roberto for the right-back slot.
Sam Marsden and Moises Llorens contributed to this report.