The 30-year-old Germany international has signed a three-year deal through to June 2029, becoming Ajax's fifth arrival of the summer following the additions of Tolu Arokodare, Marcos Leonardo, Caio Henrique and Daley Blind.
"The surprise may have been bigger for you than for me, but the past few days have been exciting. I'm happy to be here now," said Brandt.
The Eredivisie side confirmed the transfer on their official X account, sharing an image of Brandt in the club's iconic red-and-white colours alongside the message: "Welcome to Ajax, Julian Brandt."
Leeds had reportedly been leading the race for the attacking midfielder's signature and were said to have offered him a three-year contract, but Brandt ultimately chose Ajax.
Technical director Jordi Cruyff revealed the club had been in discussions with the former Borussia Dortmund star for several months and expressed his delight that the player selected Ajax ahead of other interested teams.
"Julian has chosen Ajax, and we are absolutely delighted about that," said Cruyff.
"We have been in talks for several months, and he also had the opportunity to sign for other clubs.
"With Julian, we are bringing in a top international player with a wealth of experience and a fantastic mentality. I am convinced he will add real quality to our squad."
Brandt arrives after a distinguished seven-year spell at Dortmund, whom he joined from Bayer Leverkusen in 2019 for 25 million euros. He amassed 307 appearances, scoring 57 goals and supplying 67 assists for a total of 124 goal involvements.
According to the report, both his overall goal contributions and assist tally were the highest of any Dortmund player during that period.
He also produced 50 Bundesliga assists and created 265 chances from open play, ranking fourth and third respectively across the league during his time with Dortmund.