The 22-year-old, who had a spell on loan at Darlington last season whilst making a comeback from a cruciate ligament injury, has made six appearances for his parent club this season.
Hogg is described as an energetic midfielder with tenacity, and so should fit the "Michael Brown" role very well.
Hogg describes Pompey as a "massive club" and will wear the number 14 shirt. It has not been disclosed yet if he can make his debut tonight against Burnley.