He said: "I'm buzzing, delighted to be back. I didn't really want to leave in the first place and I've jumped at the chance to come back. There were other opportunities but when I heard United was in for me this was the move. I know a lot of the lads and it will be great to get re-acquainted. I've not worked with Kevin Blackwell but I've heard good things.
"The team is flying at the moment but I want to get back into the team as soon as possible. The fans know what I'm about and I'd like to think I've improved in the year I've been away."
He left Bramall Lane in the previous January transfer window. Bromby has been brought in by Kevin Blackwell so he covers for Ugo Ehiogu who will miss the remainder of the season.