Town beat Norwich, Watford and Brighton in the race for Parkin, who - after the arrival of Reading's Nicky Forster - is the club's second signing this week.
Gorman had been second in command at Reading, but the Second Division club's chairman John Madejski allowed him to leave to resurrect his partnership with Hoddle.
Saturday's defeat left the London club level on points with bottom side Reading, who lost 2-1 at Norwich, while Stoke climbed six points clear of the relegation zone after ending a run of six defeats and a draw.