The deal could rise to €86m with another €11m in add-ons negotiated between Barca and the Dutch giants for the 21-year-old.
Manchester City and Paris Saint-Germain were apparently also keen to land five-times capped De Jong this summer, but he has opted to head to La Liga.
"FC Barcelona and Ajax have reached an agreement for the transfer of midfielder Frenkie de Jong, who will be joining the Catalan club from 1 July 2019," said Barcelona on their official website.
"The cost of the transfer operation is 75 million euros, plus a further 11 million in variables.
"The player will be signing a contract for the next five seasons, through to 2023/24.
Right footed and strong in the one-on-one, Frenkie de Jong can play either as a defensive or attacking midfielder. His wonderful vision and natural ability to find the right pass mean he is the perfect choice as a central playmaker.
"The latest addition to the Barça squad continues a long and successful tradition of Dutch players at the club, going all the way back to the great Johan Cruyff who came to the Camp Nou in 1973, and including such illustrious names as Ronald Koeman, Patrick Kluivert, Frank de Boer and current first team goalkeeper Jasper Cillessen."
Club president Josep Maria Bartomeu and CEO Oscar Grau personally oversaw the brokering of the deal in Amsterdam.
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.
Barca landed 31-year-old Ghanaian forward Prince Boateng in a sudden loan move from Serie A side Sassuolo on Monday for €1m with the option to move permanently for €8m in the summer.
They have also snapped up Valencia defender Jeison Murillo for the rest of the season.