The A's announced the deal Thursday morning before the trade deadline.
Milone requested a trade given his recent success and demotion to Triple-A Sacramento. The left-hander went 6-0 with a 2.62 ERA over 11 starts when he was sent down July 5 following the trade for Jeff Samardzija and Jason Hammel from the Cubs.
Fuld began the season with Oakland. The A's liked Fuld coming out of spring training but designated him for assignment April 12. The Twins claimed him off waivers eight days later.
He and newly acquired Jonny Gomes are likely to compete for time in left field after Yoenis Cespedes was traded to Boston for left-hander Jon Lester and Gomes.