He is the Blades' second signing of the January transfer window following the arrival of Jack Rodwell and has signed a two-and-a-half-year deal for an undisclosed fee.
Speaking of the signing of Robinson, manager Chris Wilder said: "Jack's got a great pedigree and he will make our squad stronger.
"But he isn't just coming in to make the numbers up, it's a specific position in our system and we feel he is the best option for us at this time.
"Jack can comfortably play in a couple of roles and we're delighted to add him to the group. He's got a fantastic attitude and he's ambitious to earn a place in the team."
Welcome, Jack pic.twitter.com/bD2KUGRqKF— Sheffield United (@SheffieldUnited) January 21, 2020