The 19-year old was part of the Saints academy for six years before signing a professional deal in 2011.
He has since made two first-team appearances for Nigel Adkins' men and was part of Saints' squad when they beat Boro 4-1 in the Capital One Cup earlier this season.
Hoskins, who has also had loan spells with Preston and Rotherham, could make his Stevenage debut against Crewe on Saturday.
Meanwhile, Boro's Spanish striker Dani Lopez has extended his loan stint at Aldershot by a further month.
- Sports & Recreation
- Nigel Adkins