Oldham’s win over Bolton on Saturday meant that Chris Wilder’s men were crowned champions without kicking a ball, but a fast start at home to their Yorkshire rivals proved they were worth title winners.
Leon Clarke led the way with his assured finish after 13 minutes before Billy Sharp doubled the hosts’ lead with just 20 minutes on the clock.
A second from Clarke shortly before half-time meant that the game was over before half-time as a party atmosphere engulfed Bramall Lane.
The win saw United move onto 94 points, 15 ahead of Bolton.
The 3-0 reverse was a blow for Bradford’s automatic promotion hopes, as they remain in fourth place, four points Bolton in second having played two games more.
Hundreds of home fans flooded onto the pitch as their celebrated the end of their six-year spell in the third flight.