You are not permitted to download, save or email this image. Visit image gallery to purchase the image.
Maurizio Sarri's team beat Watford 3-0 at Stamford Bridge in their penultimate game to ensure they will return to the Champions League next season but Manchester United will definitely not be joining them.
United's prospects were already slim but a woeful 1-1 draw away to bottom club Huddersfield Town ensured Ole Gunnar Solskjaer's side can finish no higher than fifth.
Arsenal then handed their London rivals Chelsea and Tottenham Hotspur a welcome gift by only drawing 1-1 at home to a Brighton & Hove Albion side whose top-flight survival had been sealed 24 hours earlier.
That meant Chelsea were guaranteed a top-four finish, while Tottenham Hotspur, whose domestic form has collapsed culminating in a nine-man defeat at Bournemouth on Saturday, are all but assured of a Champions League spot due to their superior goal difference.
While Arsenal could still match their north London rivals' total of 70 points should they win at Burnley on the final day of the season and Spurs lose at home to Everton, they must also achieve a highly unlikely eight-goal swing.
"We knew it is going to be difficult but our focus is now the Europa League," Arsenal manager Unai Emery, whose side lead 3-1 going into the second leg of their semi-final at Valencia next week, said with an air of resignation.
"We have the opportunity in the Europa League to do something important and we will try and do that."
Arsenal had taken an ninth-minute lead through Pierre-Emerick Aubameyang's early penalty but Glenn Murray's spot kick dragged Brighton level, meaning Arsenal have earned a miserly one point from the past 12 on offer.
Chelsea have not been a great deal better in an increasingly inept scrap for the top-four, picking up only two from nine points in their previous three games, and they were booed off at halftime against Watford with the score 0-0.
Quickfire headers from Ruben Loftus-Cheek and David Luiz early in the second half, both from Eden Hazard assists, put them in control and Argentine marksman Gonzalo Higuain added a third in the 75th minute.
"In the first half we were in trouble because we were tired, physically and mentally," Sarri said.
"We were lucky of course because we scored after two minutes and after the first goal, probably we improved mentally."
Sarri gave a brief substitute appearance to title-winning defender Gary Cahill for what is almost certainly his last Chelsea appearance in the league at Stamford Bridge.
Manchester United, for whom Solskjaer's impressive start after taking over from sacked former Chelsea boss Jose Mourinho in December is now a fading memory, failed to even rouse themselves for a trip to Huddersfield, who until Sunday had managed 14 points.
Looking for a first win in five matches in all competitions, United made a fast start with Scott McTominay putting them ahead.
But they deteriorated and an error by Luke Skaw allowed Isaac Mbenza to race on to a goal kick and score his first ever Premier League goal after the break.
"We've talked about next season as in we need to start to rebuild and of course next season will be one without Champions League football," Solskjaer said.
"We haven't deserved to be top four, we've chased the pack and been given chances, the league is so tight. When we got the opportunities we didn't take them."
Chelsea are 21 points behind second-placed Manchester City, who could go top with a home win over Leicester City on Monday.
Tottenham, considered title contenders as recently as January, have lost seven of their last 11 league games, evidence of just how far the chasing pack have fallen.
One fan neatly summed it up on a BBC chatroom: "As a Chelsea fan it just doesn't feel justified. We've been the best of a bad bunch," he said.