Unusually for this topsy-turvy year, everything pretty much went to script at both ends of the table with Norwich's relegation confirmed as it went down 2-0 at home to Arsenal.
City knew all it needed was a draw, due to its two-point gap and superior goal difference over second-placed Liverpool.
The Reds beat Newcastle 2-1 at Anfield but it proved of little consequence.
It was a nervy opening at Eastlands, but as news filtered through of Liverpool going behind the atmosphere relaxed and City began to find their rhythm.
Liverpool, whose title hopes rested on it beating Newcastle and an unlikely favour from West Ham, conceded in the 20th minute as Martin Skrtel diverted into his own net following a cross from the left by Yoan Gouffran.
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Champions-elect City wrapped things up either side of half-time.
Nasri gave them the breakthrough they had been searching for with a sublime drive from 25 yards that gave West Ham keeper Adrian no chance in the 39th minute, before captain Kompany prodded home from close range four minutes after the interval to get the party started.
A mad five minutes handed Liverpool control at Anfield as Daniel Agger steered home Steven Gerrard's long free-kick delivery before Daniel Sturridge scored almost a carbon copy three minutes later - with Shola Ameobi seeing red in between - but it mattered little.
Paul Dummett saw red three minutes from the end for kicking Luis Suarez to complete a disappointing afternoon for Alan Pardew's side.
After a lifeless first half Norwich slipped down to the Championship without much fuss as Arsenal cruised in at Carrow Road.
The Gunners, who can be forgiven for having one eye on next week's FA Cup final, wrapped up the win with goals from Aaron Ramsey and Carl Jenkinson.
Hull, Arsenal's opponents in next week's cup final, signed off its campaign with a 2-0 defeat to Everton at the KC Stadium.
Steve Bruce's side fell behind early on as James McCarthy scored his first goal since moving to Goodison from Wigan in the northern summer, before Romelu Lukaku ended his loan spell at the Toffees by notching his 15th of the season.
Rickie Lambert issued a timely reminder of his England credentials in front of Roy Hodgson with a cool finish in Southampton's 1-1 draw with Manchester United - as Juan Mata grabbed his sixth goal in a United shirt.
United's failure to win at St Mary's meant Tottenham would finish sixth and secure Europa League football whatever happened at White Hart Lane, but Spurs made light work of Aston Villa anyway.
They took a 3-0 advantage before half time thanks to Paulinho, an own goal from Nathan Baker and an Emmanuel Adebayor penalty as Villa fell to their 20th defeat and finished 15th.
Garry Monk's Swansea ended Sunderland's four-match winning streak, which included the scalps of Chelsea and Manchester United, by coming out on top 3-1 at the Stadium of Light.
Goals from Nathan Dyer and Marvin Emnes effectively ended the game after 14 minutes and though Fabio Borini got one back for the host, Wilfried Bony notched his 16th league goal of the season to complete the scoring.
Cardiff signed off their year in the Premier League, after its relegation was confirmed last week, with a 2-1 defeat to Chelsea.
Boyhood fan Craig Bellamy's early strike looked to be sending them away with a great result, but Jose Mourinho's Chelsea hit back with goals from Andre Schurrle and Fernando Torres.
Fulham also bowed out with a 2-2 draw at Crystal Palace. Dwight Gayle bagged a brace to take his recent tally to four goals in two games, with 19-year-old Cauley Woodrow equalising for the hosts in between, before Chris David ensured it ended all square late on.
Worryingly for Australia, Palace skipper Mile Jedinak went off with an injury in the seciond half.
West Brom brought the curtain down on a disappointing season by finishing directly above the trapdoor as Gareth McAuley's own goal and a Charlie Adam strike made it 2-1 to Stoke at the Hawthorns, Stephane Sessegnon having equalised in between times.
