Morgan-Smith was available on a free transfer after he was released by the Latics, having made only four starts for the League One club this season.
The 26-year-old has previously had spells with Stockport County, Luton, Macclesfield and Kidderminster.
"I want to try and get this club back into the Football League where they should be," he told the club's website.
Relegated Cheltenham Town have signed former Oldham striker Amari Morgan-Smith on a one-year deal.