Stearman spent last season at Wolverhampton Wanderers and had hoped to remain at Molineux having made 18 starts in the Championship.
However, Wolves passed on turning the loan spell into a permanent deal and the Blades have moved to secure the signature of the centre-back for a "substantial undisclosed fee".
Manager Chris Wilder told the club's official website: "Richard was our number one target throughout the summer and I'm delighted he has signed. We've been on the look out for a central defender who has played extensively in the Championship and who possesses the qualities and characteristics to fit in with our group.
"Richard will undoubtedly strengthen us, he's a calm influence in the dressing room and every manager who I have spoken to about him says he has outstanding leadership qualities and will offer 100% commitment, on and off the pitch. He had other opportunities to pursue, but I am delighted we have managed to tempt him to Bramall Lane."
Stearman has also enjoyed periods in the Football League with both Leicester City and Ipswich Town.