The 28-year-old is set for his Blades debut with Saturday’s visit of QPR to Bramall Lane after completing a loan move from Cardiff City.
The striker only joined the Bluebirds 12 months ago - in a £6m deal from Bolton Wanderers - but helped Neil Warnock’s side win promotion to the top flight.
Now Wilder is hoping former Sheffield Wednesday forward Madine can make a similar impact at United, and put pressure on his current strikeforce, of Billy Sharp, Leon Clarke, David McGoldrick and Conor Washington.
“Gary will be the first to know he's got a fight on his hands to get in the team,” said Wilder. “He's got to get through Billy and Didzy.
“But he'll be looking to play a big part and I'm looking for him to play a big part.”
The Blades have signed Madine and Everton midfielder Kieran Dowell on loan in the January transfer window, and Wilder has not ruled out a third addition before the end of the month.
Oliver Norwood has signed a permanent deal at United, following his successful loan move.