The 27-year-old goalkeeper will spend the 2022/23 campaign with Chris Wilder’s Championship outfit.
A 29-cap USA international, Steffen has made 21 appearances during his two seasons with City, winning two Premier League titles and the Carabao Cup in 2021.
He began last season in goal for the FA Community Shield curtain-raiser against Leicester City.
With the World Cup beginning in November, Steffen will have the opportunity of playing regular first team football at the Riverside Stadium in the coming months.
Everyone at Manchester City wishes Zack the best of luck during his loan spell.