Goode, 35, had previously signed for London Irish over the summer but was forced to quit rugby due to injury in September and never made an appearance for the Exiles. Alongside Goode's unveiling, the Falcons also announced the signing of scrum-half Jamie Booth from New Zealand side Manawatu Turbos.
Both Goode and Booth have signed three-month contracts with Newcastle following injuries to half-back pairing Delaney and Rui Tipuna, who have both been ruled out of action until the spring.