Forsyth's move will link him again with Whaddon Road manager Graham Allner, after both had spent time together at Kidderminster Harriers, and The Robins will aim to have his loan move become permanent.
The midfielder will look to help boost the fortunes of the Gloucestershire club, who have struggled since their promotion from Division Three last season.
On Forsyth's loan move, Posh manager Barry Fry said: "Richard is one of a number of our senior players who are out of contract at the end of the season.
"He wants to stay (at Peterborough), and I want to keep him, but because of the uncertainty over the sale of the club my hands are completely tied.
"I feel sorry for Richard because he has committed himself 100 per-cent to the (London Road) club."
