The former Kettering centre-back, who can also operate in midfield, is likely to make his debut in the home game against Barnet on Tuesday.
Geohaghon has had loan spells at Rotherham and Shrewsbury already this season, scoring once in 19 matches.
Gannon has been busy in the transfer market since his arrival at Vale Park, completing the loan signings of Birmingham midfielder Jay O'Shea and West Bromwich Albion strike duo Romaine Sawyers and Kayleden Brown prior to the 1-0 home defeat against Cheltenham on Saturday.
Source: BBC Sport
Source: BBC Sport