The 29-year-old was on loan at Walsall in 2016-17, making 26 starts in League One after joining the Iron in 2015.
The former Scotland youth international has also previously played for Preston, Stevenage, Torquay and Plymouth.
"I'm from Somerset so it's nice to be able to move nearer home," Laird told the Gloucestershire club's website.
"I haven't been able to do that for 10 years in my football career. It's great to be a part of something that can really kick on."
Meanwhile, Forest Green have named Helen Taylor - an ambassador for the club's sponsor - as the club's new chief executive, while long-serving supporter Phil Butterworth replaces David Drew - Stroud's new Member of Parliament - as vice-chairman.
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Newly-promoted League Two club Forest Green Rovers have signed left-back Scott Laird on a two-year deal after his release by Scunthorpe United.