Manchester United and Chelsea booked their spots in next season's Champions League but it was relegation for Bournemouth and Watford, despite valiant efforts on the final day.
United needed just a point at Leicester to secure a top-four finish but Bruno Fernandes' cool penalty and Jesse Lingard's late goal helped them to a 2-0 win to grab third place in the Premier League table, level on 66 points with fourth-placed Chelsea, who beat Wolves 2-0 with two quickfire first-half injury-time goals.
Fifth-placed Leicester, who had been in the top four for 298 days and only dropped to fifth in midweek, will go into the Europa League group stages along with Tottenham, after their point at Crystal Palace was enough to edge Wolves into seventh on goal difference.
Nuno Espirito Santo's side will now have to wait until the FA Cup final on August 1 to see whether they will be in Europe - an Arsenal win against Chelsea at Wembley would see the Gunners take the second qualifying-round place.
It was misery at the other end of the table for Bournemouth and Watford. Eddie Howe's side pulled off a brilliant and brave 3-1 win at Everton but it was not enough to lift them out of the drop zone because of Aston Villa's nervy point at West Ham.
Watford - who sacked Nigel Pearson two games ago - also fall into the Championship, finishing second-bottom and, like Bournemouth, just a point from safety, after going down 3-2 at Arsenal. Norwich - who lost 5-0 at Manchester City - had already been relegated.
Elsewhere in the Premier League on the final day, champions Liverpool signed off with a 3-1 win at Newcastle, despite resting a number of star players, Man City's big win over Norwich - in David Silva's final Premier League game - also saw Ederson win the Golden Glove, with Burnley's Nick Pope beaten in a 2-1 defeat to Brighton, and Southampton beat Sheffield United 3-1.
Neville: Now Man Utd need to invest to improve
"It's a big day for Ole. It will give him some peace. It demonstrates the progression we have seen in the last few months. The team are better, they are younger and they can play a different way now than they could at the start of the season.
"They were really basic in the sense they just played counter-attack [earlier in the season]. With Bruno Fernandes and Paul Pogba, and Mason Greenwood emerging, they look like they can play different ways and win different ways.
"But when you play the same team, that first eleven, for a week or two, they start to get fatigued. That demonstrates they need more players in the squad. The last time Manchester United finished in the top three was under Jose Mourinho and they spent £170m that summer.
"United need to invest money again but do it correctly this time. The squad needs improving, the team needs improving. First and foremost, they need to improve the first eleven."
Keane: CL spot will boost United's transfer business
"Credit to United. The performance wasn't great but it's a job well done. All credit to the United players and Ole and their staff. This was a big step for them.
"If you work at Man Utd, you'll always have money available. But regarding the recruitment, if United had not got the Champions League it would have been very difficult. All the top players have to and want to play in the Champions League, so that gives Ole better options when he goes to speak to these players. He needs to get backing and I'm pretty sure, having qualified now, he'll get that backing."
Redknapp: A great achievement for Lampard
"It's a great achievement. I said at the start of the season, if they could get top four it would be a really good one - they've done it and got to the FA Cup final as well. The progression of a lot of young players we've seen - the likes of Mason Mount, who was outstanding today, the opportunities they've been given at a club where young players haven't had a chance with other managers.
"[Lampard] will be delighted with the job he's done. He's under no illusions, there are things to address, they need to get better defenders in, get a keeper in next season but with Timo Werner and Hakim Ziyech coming, it's a very exciting time for Chelsea right now."
Vardy: European football was the target
"It was disappointing - more with the way we've ended up losing the game - but the target at the start of the season was to qualify for Europe and we've done that. Unfortunately over the course of the season [qualifying for the Champions League] wasn't meant to be. But over the summer we'll reflect on it and try to come back stronger next year."
Final day in stats
- Despite the victory, Arsenal have suffered their lowest Premier League finish (8th) since the 1994-95 campaign when they finished 12th.
- At the age of 33, Chelsea's Olivier Giroud has become the oldest player to score in five consecutive Premier League starts, taking over from Jamie Vardy (32 years old).
- Tottenham have finished the Premier League campaign in the top six for the 11th consecutive season, after managing to do so just twice in their previous 17 seasons in the competition.
- Bournemouth ended a run of nine consecutive away Premier League defeats, with this their first away win since winning 1-0 against Chelsea in December.
- Leicester finished fifth in the 2019-20 Premier League, despite ending the day within the top four places on 325 occasions during the season.
- Harry Maguire became the first outfield player since Gary Pallister in 1994-95 to start every game in a Premier League campaign for Manchester United.
- Manchester City have scored 100+ league goals in a top-flight season for a fifth time, an English record (also 1936-37, 1957-58, 2013-14 and 2017-18).
- Manchester City midfielder Kevin De Bruyne assisted his 20th Premier League goal of the season, a joint-record in the competition alongside Thierry Henry in 2002-03.
- Norwich are the third team in Premier League history to lose 10 consecutive matches, after Sunderland (20 as of September 2005) and Aston Villa (11 as of April 2016).
- This was Liverpool's 32nd Premier League win of the season, a joint-record by any side in English top-flight history (along with Manchester City in both 2017-18 and 2018-19).
- Sheffield United end the 2019-20 season having lost three straight Premier League games for the first time since April 2007.
- Aston Villa's point means they have survived relegation from the Premier League, despite failing to keep a clean sheet away from home all season - only the tenth time this has happened in a Premier League campaign.
- In 19 games under David Moyes, West Ham recorded one more Premier League point (20) than they managed in their 19 previous games this season under Manuel Pellegrini (19).
Deeney: People lose their jobs because we haven't been good enough
"You've got to look at the bigger picture. It's not today, it's not last week, it's a reflection of the whole year. We've not quite been good enough at both ends of the pitch and it showed again today.
"It's frustrating, it's disappointing, and it's heart-breaking for the people who work behind the scenes, so we feel sorry for them. I'll take the stick with regards to what comes, social media-wise, but the harsh reality is that those people will probably lose their jobs because we haven't been good enough.
"As players, we have to stand up, take that, and as a club and a community we'll go again. Individually and collectively, we haven't been good enough. From top to bottom, we'll do an audit. We'll look at where we're at, and we'll reassess."
Carragher: Lack of goals cost Bournemouth
"Bournemouth were excellent today. You're sort of scratching your head with the position they find themselves in, but they left themselves too much to do. Their away form was horrific - this is their first away win in 10, they lost the other nine.
"Before today no team had scored fewer goals from open play and you just can't fathom that from an Eddie Howe team and the players they have. They play open and expansive, that's why they concede 60 plus goals per season but even though they concede that - which makes them lose plenty of games through the season - they've always scored enough goals to keep them up. But they just haven't had that same way of opening teams up through the majority of the season."
Merson: Villa comfortable in the end
"They were very comfortable. You can't moan if you're Bournemouth and Watford, you can't just blame today's game. But you'd be disappointed if you were a Bournemouth fan and saw how West Ham played. They were comfortable and never in danger bar one long ball over the top when Antonio missed.
"It's a job done and fair play to Aston Villa, having won two and drawn two of their last four. I thought they were dead and buried. To churn out those results is a credit to the players and the manager."