The deal was reached Thursday morning, just hours after Oakland acquired All-Star pitcher Jon Lester in a blockbuster trade with the Boston Red Sox.
Milone went 6-3 with a 3.55 ERA in 16 starts this season but has spent most of this past month in the minors.
Fuld appeared in seven games earlier this season with Oakland before being claimed off waivers by Minnesota, where he batted .274 with 12 stolen bases.
Milone, 27, has been a solid starter over the past two-plus seasons in Oakland, going 32-22 with a 3.84 ERA in 73 starts.
But he became expendable after the A's added Lester to a rotation that already included Jeff Samardzija, Sonny Gray, Scott Kazmir, Jason Hammel and Jesse Chavez. Hammel, who has struggled badly since coming to Oakland from the Chicago Cubs, could be in danger of losing his rotation spot with the arrival of Lester.
Oakland received Lester and outfielder Jonny Gomes from Boston for slugger Yoenis Cespedes and a competitive balance draft pick earlier Thursday, sources told ESPN.
Fuld, 32, is a career .240 hitter in parts of seven seasons with the Cubs, Rays, Athletics and Twins.
Fuld and Gomes could be part of a platoon arrangement to replace Cespedes in left field. Fuld also gives the Athletics a solid defensive outfielder to make up for the loss of Craig Gentry, who is on the disabled list with a broken right hand.