Furness joined Becky Langley's side following the expiry of her contract with Bristol City Women.
After joining the Robins in January 2023, the Northern Ireland international helped the club win the Women's Championship title in her first season - a year after completing the same feat with Liverpool.
Previously with Newcastle United in the early stages of her career, she has also spent time abroad with Grindavik in Iceland.
On signing for Newcastle United Women, Furness said: "To sign for a club I have supported my whole life - coming back home to the North East - is a very proud moment for me. Anyone that knows me knows I bleed black and white."