"I am really excited to return to the A's and the Bay Area," Alderson said.
"His mentorship and friendship have been invaluable to me over the course of my career, and I look forward to the expertise and perspective he will add at every level of the organization," Billy Beane, A's executive vice president of baseball operations, said.
Alderson, was hired by the Mets after the 2010 season. He was diagnosed with cancer at the end of the 2015 season and had surgery, the same season the Mets lost to the Kansas City Royals in the World Series.
Alderson took a leave of absence in June 2018 after announcing his cancer had returned and said he did not deserve to return because of the team's poor record.
Alderson, 71, announced he has been cancer-free for four months while attending the New York Baseball Writers' Association of America dinner on Saturday night.
Alderson previously spent 17 seasons with the Athletics, first serving as the team's general counsel in 1981.
In 1983, he was named executive vice president of baseball operations, which saw the team win the American League pennant three consecutive seasons (1988-90), winning the earthquake-interrupted World Series in 1989 with a sweep of the San Francisco Giants.
After his time with Oakland, he also worked in the commissioner's office and was CEO of San Diego Padres from 2005 to 2009.
Alderson, who was a Marine infantry officer who served in Vietnam, is a Harvard Law School graduate.