The former Sheffield Wednesday and Bolton man agreed a loan deal for the rest of the season with Chris Wilder's men, after parent club Cardiff City granted him permission to leave.
Madine described himself as 'buzzing' to join the Blades, who are third inÂ the Championship, and claimed that United skipper Sharp advocated his return to South Yorkshire.
Madine, of course, was filmed insulting Sharp in a video that later went viral on social media but the 28-year-old said: 'I know a few lads already and I think Billy put a good word in about me to the gaffer, and said I'd be a good bit of recruitment.
'So I'm grateful for that and I'm hoping I can come and repay that faith, and score some goals.'
Madine could make his debut this weekend when United face QPR at Bramall Lane, with games against former clubs Bolton and Wednesday on the horizon.
'It'll be a bit strange being on the opposition team to Bolton and Wednesday,' he admitted, 'but I'm a Blade now. All I want to do is score goals and win; I don't care who that's against.'
Madine admitted he was 'dying to make the move happen', adding:Â 'There were other teams interested, but believe it or not when I knew Sheffield United were interested, I was buzzing and jumped at the chance.Â
'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.'
Blades boss Wilder added: '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.'