The 22-year-old had previously been playing for Norwegian club Viking and has been capped by England at under-16, 17 and under-18 level.
Green began his career at Everton where he was part of the side that won the under-18 Premier League in 2014.
He made a dozen appearances for Tranmere Rovers, then in League Two, whilst on the Toffees books, but failed to make the senior side at Goodison Park.
He went on to have spells at Oldham Atheltic, Ossett Albion and Burnley.
Whilst on Burnley`s books, Green spent time on loan at Scottish Premiership side Kilmarnock as well as at Boro's league rivals Salford City.
Green told Nuneaton`s official Pitchero website: "I am happy to get a club, this is a good opportunity and a good platform. It could not have come at a better time.
"I knew the chairman very well before this and I thought this would be a good club for me to sign for.
"It's all about playing games and playing well.
'I have been at training, I've been settling in fine and getting up to speed with the lads, learning the dynamics of the team and how they play".