Whites end on 59 points.
Rodrigo and Kalvin Phillips’ free-kick put Leeds 2-0 up at the break and Patrick Bamford converted a penalty as Marcelo Bielsa’s side, roared on by an 8,000-crowd, kept their foot on the gas all the way to the finish line.
West Brom substitute Hal Robson-Kanu struck a late consolation for the visitors, but the day belonged to Leeds, whose players saluted their fans on a lap of honour after the final whistle.
England man Kalvin Phillips missed the acclaim, though, as he appeared to suffer a shoulder injury just before the final whistle, two days before the Euro 2020 squad is announced.
Leeds closed the season in ninth and on 59 points, the most by a promoted top-flight club since Ipswich in 2000/01, and with 62 goals, a record-extending total for a promoted club in a 38-match season.
They also became the first promoted club to win their final four Premier League games in a fitting and emotional finale for players and fans alike.
Supporters passed through the turnstiles for the first time since March 2020, while Pablo Hernandez and Gaetano Berardi bade farewell as they both started in their final appearances for the club.
Hernandez, the club’s player of the year for the last three seasons, crossed for Jack Harrison to convert in the seventh minute, but the winger was offside.
Rodrigo headed home Raphinha’s 18th-minute cross for his seventh goal of the season to put Leeds in front and the home side went on to dominate the first half.
West Brom defender Darnell Furlong’s header was saved by Kiko Casilla and Callum Robinson fired a low shot wide.
But Leeds doubled their advantage in the 42nd minute. Hernandez was fouled by Conor Gallagher on the left edge of the penalty area and Phillips curled home his free-kick, his first Premier League goal, inside the near post.
Patrick Bamford replaced Rodrigo for the second half and Hernandez’s drive forced Sam Johnstone into a flying save before West Brom midfielder Matt Phillips’ shot hit the inside of a post.
The game panned out into one typical of Leeds’ season. Robinson’s low shot was well saved by Casilla and Hernandez was denied again by Johnstone at the other end.
That was the Spaniard’s final act in a Leeds shirt as he and Berardi were replaced by Pascal Struijk and Tyler Roberts with 20 minutes left. Both players were hugged by their team-mates and given a standing ovation.
Luke Ayling and Roberts both had fierce shots saved by Johnstone and Leeds extended their lead in the 79th minute when Bamford slammed home a penalty after Okay Yoksulu had handled Harrison’s cross.
It was Bamford’s 17th Premier League goal of the season and sealed West Brom’s 22nd league defeat in manager Sam Allardyce’s final game in charge.
Robson-Kanu pounced on a defensive mix-up in the closing stages to slot home West Brom’s consolation.
But the Baggies, whose immediate return to the Sky Bet Championship was confirmed two weeks ago, lost a fourth league game in a row for the first time since March 2018.