The move effectively ends Hussey's time at Bramall Lane, as the loan covers the entire 2017/18 EFL season and the left-back's Blades contract will expire after that.
The 28-year-old signed from Bury last summer but made only eight appearances in all competitions as United won the League One title.
Blades boss Chris Wilder said: "Chris goes to Swindon looking for some regular first-team football under a manager he knows. We wish him all the best."