Peterson previously had spells for Scarborough Athletic, Barnet and Doncaster Rovers before making his move to Northern Premier League side Belper Town in 2018.
The 27-year-old appeared in 35 games for the Nailers last season, scoring ten goals for the East Midlands side.
The forward has the ability to play through the middle or left of the attack, adding firepower to manager Ryan Cresswell’s outfit.
Sheffield currently sit 13th in the NPL East Division, with nine points from their opening eight games this season.
The fans will hope the addition of Peterson will aid the side in climbing out of the bottom half of the table.
Peterson could make his home debut at The BT Local Business Stadium on Tuesday as Sheffield welcome Brighouse Town.
Photo credit Sheffield FC
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