Watford and Bournemouth suffered relegation.
Manchester United and Chelsea both secured qualification for the Champions League on the final day of the Premier League season.
United finished third thanks to a 2-nil win over Leicester - Bruno Fernandes and Jesse Lingard with the goals.
Manager Ole Gunner Solskjaer says his players will need to raise their level next season when they face better opposition in Europe:
Leicester will play in the Europa League next season after Chelsea claimed fourth place with a 2-0 win over Wolves at Stamford Bridge.
Aston Villa secured their Premier League status with a 1-1 draw away to West Ham.
That result relegated Bournemouth and Watford to the Championship.
Watford went down after losing 3-2 at Arsenal, while Bournemouth's 3-1 win at Everton wasn't enough to keep them up.
Villa manager Dean Smith believes his side benefitted from the three-month enforced shutdown:
Elsewhere, champions Liverpool finished off the season with a 3-1 win at Newcastle
Second placed Manchester City beat Norwich 5-0 at the Etihad in David Silva's final league game for City.
Tottenham's 1-all draw with Crystal Palace means that Jose Mourinho's side will play in next season's Europa League.
Aaron Connolly scored for Brighton in their 2-1 win at Burnley
and Southampton came from a goal down to beat Sheffield United 3-1.