This victory ensures that they will finish second in the Championship behind champions Burnley.
The Blades, coached by Paul Heckingbottom, will return to the Premier League after two seasons, having been relegated in the 2020-21 campaign in which they finished bottom of the table.
The Yorkshire club is currently second in the second-tier standings on 85 points after 43 games, 10 points behind Burnley, who clinched the title on Tuesday by beating local rivals Blackburn Rovers.
Sander Berge and Anel Ahmedhodzic scored the second-half goals that guided Sheffield United to victory over West Brom, taking an unassailable seven-point lead over third-placed Luton Town, who have played 44 games.
"We've worked so hard for this all year, and to do it at home in front of our own crowd is so special," said Berge in a post-match interview with Sky Sports. "We want to give back to the club and fans. I came here when we were in the Premier League, and now we're back where we need to be."
Sheffield United missed out on promotion last season after losing to Nottingham Forest in the playoffs. However, the top two teams in the division are promoted to the Premier League while the teams that finish third to sixth go into the playoffs to fight for the final spot.
Promotion can be worth over 300 million pounds ($373.95 million) over five seasons if a club survives their first season in the Premier League, according to last year's Deloitte Annual Review of Football Finance.