The 23-year-old, who can also play out wide, was at Burton Albion until he was 16 before being bought by Blackburn Rovers for the rest of his traineeship, and then turning professional at Ewood Park.
He left Rovers at the end of the 2015-16 season and then went to Hednesford and Stourbridge before a move to Tranmere Rovers, who paid a fee for his services.
In June 2018, he joined Southport on a two-year deal and has scored 10 goals in 24 appearances so far this season for the National League North side.
Green takes the No 33 shirt.