The 32-year-old Scarborough-born schemer, who can play anywhere across the midfield four, began his career at York City before spending three years at Manchester United.
Greening has also played for Middlesbrough and West Brom, and was a fans' favourite at The Hawthorns where he was skipper for most of his spell there.
However, he only made 10 league appearances for the Cottagers last season and his move to the City Ground should ensure him more first-team football.
Greening followed new Forest boss Steve McClaren to Middlesbrough from Manchester United when he took charge at the Riverside in 2001.
He will reportedly cost McClaren around £600,000 this time and is a contender for the captaincy this season following the release of Paul McKenna.