Collins originally joined Leeds on loan in 2010 before United made his move permanent on the eve of the new season. He has made 23 appearances this term.
Simon Grayson said: "We had an offer from Sheffield United which we felt was good for the club. We gave the Neill that option, and although he's disappointed to be leaving, he has taken it. He hasn't been in the team and he wants to play football.
"Opportunities have been limited for Neill, we've got other players who are in there and this may give him the chance to play regular football. He goes with all our best wishes and thanks for what he did at the end of last season and what he has done so far this season."
Collins has a wealth of experience and has previously enjoyed spells with Queen's Park, Dumbarton, Sunderland and Wolves.
Sheffield United are looking to rebuild under Micky Adams and have conceded 43 goals in 27 league games this season.