Southampton's 1-0 victory over Swansea City ended the Midlands club's eight-year stay in the top flight.
West Brom have been rejuvenated in recent weeks, winning three games in an unbeaten five-match run, but their revival came too late in the campaign.
Southampton's win moved them onto 36 points, leaving West Brom five points adrift of the safety zone with one match to play.