The 26-year-old pacey winger joins Latics having spent the first-half of this season with AFC Telford United.
"I'm delighted to get the deal over the line, and can't wait to get started," he said.
"I tend to play on the wing, I like to get at players, and hopefully I can bring a lot to the team."
Green came through the youth set-ups at Burton Albion and Blackburn Rovers, before being released in 2016.
Having spent time with Hednesford Town and Stourbridge, he was rewarded for his good performances by getting a move to Tranmere Rovers in 2017.
After failing to establish himself in the first-team, he moved to National League side Southport, spending two seasons at Haig Lane, making over 60 appearances.
Green then joined Scunthorpe United in January 2020, and was a regular on the wing during the 2021/22 season, scoring three goals.
He left Scunthorpe in March 2022 to join Telford United.
