The 21-year-old midfielder recently joined the Latics from Rangers on a two-year deal after making just one first-team appearance as a substitute in three years at Ibrox.
Furman had been offered an extended stay with the Scottish Premier League champions after impressing during a 33-match loan spell with Bradford last season, but opted to join Oldham.
Penney said: "He's a good age, he got some good experience with Bradford and is ready to step up a level with us.
"I know Bradford were very keen and that says something about Dean, but once we'd spoken to Dean I knew he'd come here.
"He did very well with Bradford and I'm confident he will continue his progress at the higher level."