The signing of the 23-year-old midfielder continues the strengthening process of the squad under new Head Coach Carla Ward.
Green is best suited to playing in the number 10 role but can also figure on the wing or in a deeper midfield position.
Hailing from Merseyside, the former England Under-19 international began her footballing journey as a youth player with Liverpool.
Having made the step up into the senior side, where she made just a solitary appearance, she later joined local rivals Everton in 2017.
After a season with The Toffees, during which time she made 20 appearances and scored three times, she joined newly formed Championship side Manchester United in their debut season.
During that campaign she found the back of the net an impressive 13 times in 18 games; including bagging a hat-trick in an 8-0 victory over Millwall.
In January 2020 she was loaned to Sheffield United - playing under Ward - and scored twice in her three matches before the season was curtailed because of Coronavirus.