The 32-year-old had been playing in the Isthmian Premier Division with Leatherhead following his release by Newport at the end of last season.
Pidgeley has made 260 appearances in spells with nine clubs, including Chelsea, Watford and Millwall.
Forest Green are currently second in the National League table, one point behind leaders Cheltenham Town.
Pidgeley could make his Rovers debut when they host Aldershot on Friday.

Those who saw a drop in enquiries last month outnumbered those who saw a rise by 22%.
That is the highest figure reported by the Royal Institution of Chartered Surveyors (Rics) since August 2008.
Rics said the main reason was the stamp duty rise on 1 April, and the uncertainty around the EU referendum.
The number of new enquiries fell most dramatically in London, but also fell in nine other regions of the UK.
Enquiries rose only in East Anglia, the North and Scotland.
Most surveyors also reported a fall in new instructions to sell, and most expect prices to rise over the next three months.
Rics chief economist Simon Rubinsohn said the market was characterised by uncertainty.
"More ominous is the expectation that both prices and rents will head materially higher over the medium term," he said.
Earlier this week the Halifax reported that annual house price inflation fell from 10.1% in March to 9.2% in April.
National League side Forest Green Rovers have signed goalkeeper Lenny Pidgeley until the end of the season.
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The number of people interested in buying a house in April fell to its lowest level for nearly eight years, according to surveyors across the UK.