Edwards, 27, who can play in defence or midfield, played before for Barwell and Nottingham Trent University.
"He's been a standout performer over the last couple of seasons and will be an asset to the squad," Solihull manager Liam McDonald said.
Edwards becomes Solihull's fifth signing this week following the arrivals of Luke Benbow, Chris Lait, Kalern Thomas and Shomari Barnwell.
Meanwhile, midfielder Shep Murombedzi has agreed a new one-year deal with the National League side.
Find all the latest football transfers on our dedicated page.
Solihull Moors have signed Jack Edwards from Leamington on a one-year contract.