The Eredivisie club added the agreement, which is reportedly for a fee around $17 million (£14m), is subject to a medical.
Ajax director for football Marc Overmars had previously talked up the possibility of the club moving for the Alvarez, saying the 21-year-old was a target for them regardless of the situation regarding Matthijs de Ligt, who has since had his move to Juventus confirmed.
"I think he has the right age - 21 years old, he's a regular starter for the Mexico national team and we know him very well because we've been following him for quite some time now,” Overmars said. “He's had good development, and he's versatile."
The Mexico international developed as a center back at the club level, but has since featured at right back internationally, though this summer saw him move into a holding midfield role for Tata Martino’s El Tri squad.
Alvarez had spent the entirety of his young career with Liga MX side America, who released a statement on Twitter thanking the versatile defender for his contributions to the club.
"You helped us with our dream of winning a 13th title, and now it's our turn to support you with your dreams. Thank you, Edson Alvarez, and here's to much success with Ajax," the tweet said.
You helped us with our dream of winning a 13th title, and now it's our turn to support you with your dreams.— Club América EN (@ClubAmerica_EN) July 19, 2019
Thank you, @EdsonAlvarez19, and here's to much success with @AFCAjax!#FlyWithUs pic.twitter.com/YEfzcAAFEQ
Alvarez broke into America’s senior side during the 2016-17 season, playing 21 times and scoring a pair of goals.
He remained a key contributor for the club over the next two seasons, appearing in 31 and 34 Liga MX contests over those campaigns respectively.
In 2018-19, Alvarez also added his first bit of silverware to his trophy case, earning both the Liga MX title when America defeated Cruz Azul in the 2018-19 Apertura, as well as the Copa MX.
Alvarez enjoyed international success this summer, starting five of Mexico’s Gold Cup contests, including the final where El Tri triumphed over regional rivals the United States by a 1-0 scoreline to take back the Concacaf crown.
He will hope for success similar to international team-mate Hirving Lozano, who has starred for Ajax’s rivals PSV in two seasons in the Eredivisie.