Goals from Michail Antonio and Nile Ranger saw the Owls return to the second tier after a two-year absence in front of 38,082 fans.
United drew 2-2 at Exeter, and with Wednesday winning, it was not enough.
Antonio struck in the 25th minute to calm nerves at Hillsborough. Wednesday needed to either win or match United's result to go up behind division winners
Dave Jones's side never looked in danger: they dominated the match, earning 55 per cent of the possession and 18 shots. Wanderers had only three shots, and none on target.
United went behind on 24 minutes, Alan Gow scoring for the Grecians, but Lee Williamson and Kevin McDonald were on target on 44 and 47 minutes for the Blades to worry Owls fans.
However Ranger struck on 52 minutes to ensure that the blue half of the Steel City would be celebrating - and Scot Bennett equalised for Exeter in injury time to rub United's nose in it.
The Blades now enter the play-offs, and will play
Exeter and Wycombe were already relegated before the day's fixtures, as were already relegated before the day's fixtures, as were Rochdale and Chesterfield.
The latter sides ended their stay in the third tier with defeats.
In the other final-day matches,