The 20-year-old, who also captained England's U20 side at this summer's World Cup, will spend the next six months with the League One club.
Coady appeared twice for Liverpool's first team last season, starting a Europa League tie at Anzhi Makhachkala and coming off the bench at Fulham in May.
He can play in defence or midfield and becomes the sixth new arrival at Bramall Lance since David Weir was appointed manager.
Weir told the United website: "I've been aware of Conor's talents for a long-time, through his development with Liverpool and England and he is a great prospect.
"He will add competition for places in the midfield and will be an asset for us."