The 28-year-old has signed for United on loan until the end of the season, from Premier League side Cardiff City.
Madine passed a medical at the weekend and watched from the stands as his new team crashed out of the FA Cup, losing 1-0 at home to Barnet.
“I sign the players for this football club and I try and get as many right as possible," manager Chris Wilder said.
"Generally we’ve got things right and I’m more than positive, more than happy with this signing.
“Gary gives us a physicality at the top of the pitch, tactically he gives us something different, which we’ll need in the second part of the season.
“If you ask any of our centre-halves for their opinion of playing against Gary Madine, they’ll all say the same, he’s a tough boy to play against. He is physical and technically very good too, hopefully he’ll be able to get on the end of some of the crosses we put in.
“I’m looking forward to working with Gary, he’s won promotion with Bolton and scored goals there. And if anyone knows anything about a striker it’s our old manager (Neil Warnock), he took a punt on him last season and was part of the Cardiff squad that went up.”
Madine added: “There were other teams interested, but believe it or not when I knew Sheffield United was interested, I was buzzing and jumped at the chance. I’ve played with some of the lads and against them too, I was dying to make the move happen.
“Some people have this perception I don’t like Sheffield United, but that’s not true. I’ve had over 20,000 supporters booing me when I’ve played here before, it’s an intimidating place to come and some players would crumble.
“But I’ve always thought I wouldn’t mind being part of that and it is certainly a club on the up, one who play some excellent football.”