Centre-half Green started his career with Lincoln City, before spells with Lincoln United, Granthan Town, Sheffield FC and Eastwood Town.
The 23-year-old joined Whitecaps in February 2016 after two seasons with Swedish fourth tier side Ange IF FC.
He could make his league debut for the Lions when they travel to Woking on 17 December.
National League strugglers Guiseley have signed defender Elliot Green from Canadian side Whitecaps.