The 21-year-old will sign a five-year contract with the club in a transfer worth an initial €75 million with a further 11 million in add-ons, the Catalans confirmed in a statement.
Club president Josep Maria Bartomeu and CEO Oscar Grau personally oversaw the brokering of the deal in Amsterdam.
Spanish media reports said Barcelona had beaten off competition from Paris St Germain to sign De Jong, while Premier League Manchester City had also been linked with a move for the midfielder.
De Jong joined Ajax in 2015 from Willem II and quickly set about securing a place at the base of the club's midfield, playing a pivotal role as they reached the 2017 Europa League final, where they lost to Manchester United.
De Jong is Barca's fourth signing in what is proving to be a busy January after the loan arrivals of Jeison Murillo and Kevin-Prince Boateng.
The club also announced that Jean-Clair Todibo will join from Toulouse in the close season, while Munir El Haddadi left the club to join Sevilla.
De Jong will have a chance to endear himself to Barca fans when Ajax meet Real Madrid - Barca's arch-rivals - in the Champions League next month.
(Reporting by Joseph Cassinelli; Editing by Toby Davis)
