The Blades this week signed the 28-year-old on loan from Premier League side Cardiff City.
Wilder had been desperate to bring in a striker in January to bolster his forward line as third-placed United chase promotion from the Championship.
But the signing of Madine – a controversial figure in his time at neighbours Sheffield Wednesday – has divided opinion among Blades’ supporters.
Madine, then playing for the Owls, was sent to prison for 18 months in 2013 for assaulting two fans in separate attacks in Sheffield nightclubs.
On his release he joined Bolton Wanderers before Cardiff paid £6m for the striker 12 months ago.
Now Wilder hopes Madine can replicate the impact he had on Neil Warnock’s team and help the Blades follow the Bluebirds into the Premier League.
And the Blades boss has called for supporters to trust his judgment in bringing Madine back to Sheffield.
“I am not daft, I am not going to bring someone in who is going to wreck my football club,” said Wilder. “An unbelievable amount of hard work has gone into getting us into this position, possibly more than any other club in this division.
“I have not had £50m to spend, an open chequebook. We have had to work extremely hard on the training ground, recruitment, game to game, to get into this position.
“It might split and divide opinion because of what’s happened in the past. I understand that it’s a game based on opinions.
“I’d like to think I’ve gained the support and trust of the supporters with my background, and my knowledge of the club and the supporters and the league, what’s available and what we need to go forward.
“I’ve made the decision, and it’s my decision. I understand it might not be backed fully, but people must look at the bigger picture with what we’re trying to achieve, and Gary helps that.
“He’s had a couple of promotions with Cardiff and Bolton and adds to our forward line, gives us something different in the second part of the season and will play a part in us improving, going forward.”
Gateshead-born Madine signed for the Owls in 2011, netting 26 goals in 67 league starts.
He was booed and jeered playing for Bolton at Bramall Lane last season, but he grabbed the winner.
Wilder has never been afraid to sign former Wednesday strikers, Madine following the same path as Caolan Lavery and Leon Clarke in arriving at Bramall Lane.
The striker’s decision to reject several other Championship offers, preferring a return to the Steel City, also impressed Wilder.
“Gary wanted to come,” he said. “He had the b**** to do it, he could have taken the easy way out and joined another club.
“That’s got to be admired and supported. I think the majority of our punters are really fair and understand that what’s gone off in the past, he’s played at the other side of the city, he’s done some daft things in the past.
“But to want to come to the football club and play, he gets my support, and I’d like to think the majority of our support.
“We have to trust that Gary is going to be good for the football club.
“He has turned down top clubs in this division. There are five or six clubs in this division who would have taken him, two or three in and around us.”
Wilder has brought in Madine and Everton’s Kieran Dowell on loan this month to strengthen his side’s promotion credentials.
The Blades are just two points off the automatic promotion places, and second-placed Norwich City, with 20 games remaining.
Both loan players are set to be included for tomorrow’s visit of Queens Park Rangers to Bramall Lane.
The Blades picked up maximum points from their three games over Christmas, winning at home against Derby County and Blackburn Rovers before victory at Wigan.
Wilder revealed Madine has not been immune to some dressing room banter as he quickly integrated himself with his new team-mates.
“When he walked into the changing room he knew half of the lads and has played against the other half,” said Wilder.
“There’s been a lot of mickey taking going on, 100 per cent. The changing room runs itself. We all know what makes players tick and the wind-ups.
“Bringing good players in, that shakes the rest of the group up too. We’ve done that with Gary and Kieran.
“He’s bullied people before, that’s part of the game, but he can play as well. His technical ability is good. It’s a positive signing in an extremely difficult market.
“I genuinely hope supporters put their personal things aside because if any group deserves full backing it’s this group. The players have been full tilt.
“If you look at the effect the support has had over the last two home league games, if there was ever a snapshot of what support can do, it was then.
“If we can replicate that then we’ll be in with a shout of winning a lot of those games.
“Surely that has to be the over-riding aim of everyone connected with the club.”