Liverpool, who were home league winners last season, beat Crystal Palace 2-0, while Leicester City’s 4-2 home loss to Tottenham meant Chelsea secured fourth place in the table, despite losing 2 -1 at Aston Villa.
This means Leicester again missed out on a place in Europe’s premier competition next season and qualified for the Europa League instead.
A six-game losing streak in seven matches in February and March had threatened to leave Liverpool without a Champions League spot.
But Jurgen Klopp’s side finished the season unbeaten in their last 10 games, winning eight of them. They finished in third place.
The game was Palace’s last game in charge for their manager Roy Hodgson, the former England boss who had a brief stint with Liverpool.
He left the role at the age of 73 and will occupy a place in the new government fan-led review Game.
Manchester City and Manchester United had already reserved their places in the top European competition after finishing first and second in the Premier League respectively.
Chelsea are set to face Man City in the final of the current Champions League campaign on May 29.
The match was originally scheduled to be played in the Turkish city of Istanbul.
But it was moved to Porto in Portugal after the UK government placed Turkey on its red list of countries at risk and urged fans not to travel for the game.
British citizens returning from Red List countries are required to self-quarantine in a government-approved hotel for 10 days.
Portugal is on the government’s green list, so UK visitors will be able to visit and will not need to self-isolate on their return.
At the bottom of the Premier League table, Fulham, West Brom and Sheffield United have all been relegated and will play in the league next season.