The three teams were separated by just one point heading into Sunday and Chelsea beat Wolves 2-0 at home to book one of the spots with both goals coming in first-half injury time.
That meant Leicester needed to beat Manchester United for the other place but instead it lost 2-0 at home thanks to a Bruno Fernandes penalty in the 70th minute after opposing striker Jamie Vardy — who still finished as the league’s top scorer — hit the post.
It was United’s record 14th penalty of the season and Fernandes has never missed one at the highest level, according to Sky.
Former United defender Jonny Evans was sent off in injury time for a foul on Scott McTominay, with Jesse Lingard later adding the second goal.
Manchester United and Chelsea finished on 66 points — United got third with a better goal difference — and Leicester City 62.
United was set to lose around £70 million ($90 million) had it missed out on the top four but flourished in the league since it restarted in June after being halted due to the coronavirus pandemic. Much of that was down to attacking midfielder Fernandes, who was signed from Sporting Lisbon in January.
The Red Devils trailed Leicester by 11 points in January.
“I think the boys have done a great achievement,” United manager Ole Gunnar Solskjaer, under pressure in January when results dipped, told Sky. “Where we were earlier in the season, to end up third is fantastic by them. They’ve taken on board so many things. Had our ups and downs.
“It of course came down to the last game and it’s a wonderful achievement by everyone.”
Leicester manager Brendan Rodgers said on the eve of the game it would still be a good season for his side if it didn’t qualify for the Champions League but he is sure to be bitterly disappointed.
Not only did Leicester lead United by double digits but in December it held a 14-point cushion in the race for the top four. Leicester didn’t beat any of the sides that finished in the top five all season, though sustained key injuries down the stretch.
“I can’t fault the spirit,” Rodgers was quoted as saying by the Leicester Mercury. “Next year it’s about ambition.”
Chelsea wasn’t considered a top four favorite as it dealt with a transfer ban but in his first season as manager at Stamford Bridge — after a glorious, trophy filled playing career for the Blues — Frank Lampard is on course for an impressive double.
Next week Chelsea will win the FA Cup if it defeats Arsenal.
“It means a great deal” to finish in the top four, Lampard told Sky. “I suppose at Chelsea we have to be careful getting excited with top-four finishes but coming into the job I don’t think a lot of people put us in that bracket.”
Aston Villa stays up
At the bottom of the table, Watford and Bournemouth suffered relegation to join Norwich City, which was already relegated.
Aston Villa’s 1-1 draw at West Ham meant it finished on 35 points, one more than Watford and Bournemouth.
Watford fell 3-2 at Arsenal despite an impressive fightback from 3-0 down while Bournemouth’s 3-1 win at Everton wasn’t enough to see the Cherries stay in the division.
Elsewhere, champion Liverpool didn’t start its potent front three of Mohamed Salah, Sadio Mane and Roberto Firmino at Newcastle but rallied for a 3-1 win to finish on 99 points, one more than Manchester City’s tally from last season.
Newcastle scored in the first minute through Dwight Gayle before towering defender Virgil van Dijk leveled before halftime, Divock Origi netted in the 59th minute and Mane in the 89th.
Second-place Manchester City crushed Norwich 5-0 in Spanish playmaker David Silva’s last league game for City after 10 years at the club.
Silva didn’t score despite several good chances. Kevin de Bruyne instead scored twice and picked up his 20th assist to tie Thierry Henry for the league record.