Sunderland were relegated from the Premier League following a 1-0 defeat at home to Bournemouth on Saturday.
Joshua King netted a late winner to send the Wearsiders down and end their 10-year stint in the top flight.
Neither side had been able to find the breakthrough at the Stadium of Light, with Bournemouth goalkeeper Artur Boruc making a string of fine saves and Jermain Defoe wasting several presentable opportunities for David Moyes' men.
Hull's 0-0 draw at Southampton looked to have prolonged Sunderland's stay - for another week at least - but King finished off a clinical Bournemouth break to send the hosts down to the Championship.
Sunderland have won just five games all season and, unlike in recent seasons when miraculous fightbacks late in the campaign saved the club from the drop, this time they were left with too much to do.