De Jong will link up with his new club in July this year having signed a five-year contract, and the deal could include a further €11 million (£10m/$12m) in add-ons.
In the wake of Barcelona's third signing of the Januray window, following the arrivals of Kevin Prince Boateng and Jeison Murillo, the club's president Josep Maria Bartomeu tweeted: "With the arrival of Frenkie de Jong we add talent, youth and Barça style to our sporting project.
"We are convinced that he will be a key part of our team for years to come. Welcome, Frenkie!"
De Jong follows a number of former Ajax players to join the Liga club, with Johan Cruyff, Ronald Koeman, Patrick Kluivert, Frank de Boer and Luis Suarez among the most successful to have played for both sides.
The Netherlands international playmaker has scored three goals and bagged one assist in the Eredivisie this term, after picking up seven assists last season.
Although his preferred role is in midfield, he has featured at centre-back for Ajax in the past and is known for his versatility.
What you've all been waiting for... pic.twitter.com/gDE1mujM— FC Barcelona (@FCBarcelona) January 23, 2019
His team-mate at the Dutch club Matthijs de Ligt, who won the Golden Boy award back in December, has also been linked with a move to Barca as well as Man City, PSG and Juventus.
The centre-back's future is yet to be decided, but City are reported to be the most likely destination for the 19-year-old at present with Pep Guardiola a keen admirer of De Ligt's ability to play out from the back as well as his defensive strength.