The 30-year-old was on loan at Burton Albion last season, helping them to automatic promotion to the Championship, and Wilder is a big fan after capturing Duffy on a free transfer.
“In our opinion, Mark was the best player in this division last season and we are delighted to have captured his services,” said new Blades boss Wilder.
“Importantly he knows what it takes to get out of League One, which is crucial.”
Former Doncaster Rovers winger Duffy has agreed a two-year contract at Bramall Lane, after signing a pre-contract agreement. He will officially join the Club on a free transfer on the 1st July, following his release by Birmingham City.
Wilder said: “He comes here for all the right reasons, he has come here because after listening to us he believes in what we are trying to do, Mark could have moved elsewhere for a significantly better contract.
“Mark scored and created a good number of goals for Burton, he deservedly was named in the divisional team of the year and is a player we believe can make an impact immediately and also make the step up to the division above.”
United have also signed Bury left-back Chris Hussey, 27, on a two-year deal for an undisclosed nominal fee.
Wilder said: “Chris was another really consistent player in this division last season and we are delighted to have brought him here.
“He offers us balance, versatility and a good knowledge of the league; in addition we believe he is capable of making the step up to the Championship.
“Chris is a good age and a player we have monitored and tracked for a number of years.”
Both deals are subject to Football Association and Football League clearance.