Darren Moore's men needed the game at the Liberty Stadium to end in a draw to keep their survival hopes alive, but Manolo Gabbiadini's winner confirmed West Brom's relegation.
The Baggies go down despite a 1-0 win over Tottenham on Saturday, a result that extended their unbeaten run to five games.
The club joins Stoke City, who were relegated on Saturday after they lost 2-1 to Crystal Palace , in dropping from the top flight.
West Brom will head to the Championship after an eight-year stay in the Premier League, having last played in England's second tier in the 2009-10 campaign.
Relegation is the result of a turbulent season for the Baggies, who started the campaign slowly and sacked manager Tony Pulis in November .
Pulis' replacement Alan Pardew was also sacked after a run of poor results , and caretaker manager Moore took over for Pardew in April.
Moore did all he could to guide the Baggies to a miraculous late escape, winning three and drawing two of his five games in charge.
However, the club's late surge still was not enough to keep them in the top flight.