Chelsea confirmed they will play in the lucrative Champions League next season after a 2-0 over Wolves meant they finished fourth.
Manchester United joins them in European football’s premier competition after winning 2-0 at Leicester City, who finish fifth, despite spending much of the season in the top four.
Leicester will play in next season’s Europa League along with Tottenham Hotspur and Wolves, who finished sixth and seventh respectively.
Watford, Bournemouth and Norwich City lost the fight to retain their place at the top table and were relegated to the Championship on a dramatic final day of the season.
The three relegated clubs will be replaced by three teams from the Championship. Leeds United were the first promoted team, followed by West Brom.
They will be joined by one of Brentford, Fulham, Cardiff or Swansea, with the final promotion being decided through the play-offs.
Aston Villa, who were seven points from safety earlier this month. have survived, finishing a point above the bottom three after a 1-1 draw with West Ham.
Watford, who have had four managers this season, were beaten 3-2 by Arsenal while Bournemouth beat Everton 3-1.
Both sides have had five years in the top division of English football, but now join Norwich, who were already down, in returning to the Championship next season.
The 2020-21 Premier League start date is Saturday September 12. The date was confirmed on July 24.