The Gunners’ challenge finally evaporated after a second consecutive defeat left Mikel Arteta’s side four points adrift of City with one game left for them to play.
Taiwo Awonyi’s first-half goal also ensured Forest avoided relegation in their first season back in the top flight for 23 years.
City’s third successive English title has turned today’s league game at home to Chelsea into a celebration match.
Pep Guardiola’s men will now look to complete a treble when they face local rivals Manchester United and Italian giants Inter Milan in next month’s FA Cup and Champions League finals respectively.
City have become the dominant force in the English game since an Abu Dhabi-backed takeover transformed their fortunes in 2008.
But admiration for the quality of their football under manager Guardiola has also been accompanied by questions over their financing, with City facing a mammoth 115 charges for breaking Premier League rules.
Nevertheless, City captain Ilkay Gundogan insisted his side had been pushed hard this season.
“The Premier League is without doubt the most demanding and competitive league in the world so that tells you everything about what an achievement this is,” he said.
But for Arsenal manager Arteta, a former assistant to Guardiola, there were thoughts of what might have been for the longtime leaders.
“First of all congratulations to Manchester City for winning the championship but it is a sad day for us,” Arteta told Sky Sports.
“Now we have to face the reality, today we gave a goal away and we were not good enough to break them down. We could play for three hours and we would not have done it.”
By contrast, Forest manager Steve Cooper told the BBC: “We limited them (Arsenal) to very little, incredible desire and we got over the line. It was everything we wished for from today. It is what the players and the supporters particularly deserve.”
Man Utd, Newcastle eye Champions League
Manchester United and Newcastle were on the brink of qualifying for next season’s Champions League after Liverpool’s 1-1 draw against Aston Villa.
United’s 1-0 victory at Bournemouth, combined with Liverpool’s failure to beat Villa, left Erik ten Hag’s men and Newcastle within touching distance of ensuring top-four finishes.
Fourth-placed United and Newcastle, in third, are both three points clear of fifth-placed Liverpool, who have only one game left.
At the Vitality Stadium, United took the lead in the ninth minute through Casemiro’s acrobatic bicycle kick from close-range.
“We are nearly there, but we are not there. I don’t care what happens in Liverpool, it’s about us,” Ten Hag said.
Liverpool boss Jurgen Klopp watched from the stands at Anfield as he served a touchline ban following his recent rant about referee Paul Tierney.
Villa wasted a 22nd minute penalty when Ollie Watkins fired wide after the striker was brought down but they still went ahead five minutes later through Jacob Ramsey’s volley.
Fans’ favourite Roberto Firmino, set to leave Liverpool at the end of the season, came on late in the game and the Brazilian forward then marked his Anfield farewell with a close-range finish in stoppage-time.
Everton late show
“We would have loved to make it exciting for another week, but we will make the Europa League our competition. I am not that spoilt,” said Klopp.
For Liverpool’s local rivals Everton, dreams of European football have long been replaced by the need to avoid relegation.
Yerry Mina’s last-gasp equaliser in a 1-1 draw with Wolves boosted the Toffees’ hopes of avoiding playing in the second tier for the first time since 1954.
Sean Dyche’s men fell behind after 34 minutes when Hwang Hee-chan netted from close-range.
Mina bundled in Everton’s leveller nine minutes into stoppage-time to leave them fourth bottom, two points above the relegation zone, with Leeds and Leicester snapping at their heels.
“If you are a footballer you can’t just sign up for the good things,” said Everton manager Dyche. “You have to fight to be in the Premier League and we are fighting.”
Tottenham’s season to forget hit a new low with a 3-1 home defeat against Brentford.
Spurs took the lead through Harry Kane’s 28th league goal this season, but a Bryan Mbeumo brace and Yoane Wissa’s late strike left them floundering in eighth place.
Frustration has mounted throughout the final weeks of a troubled season for Tottenham and fans hung banners outside the stadium pointing the finger of blame at owners ENIC, while chanting for chairman Daniel Levy to resign.
Fulham and Crystal Palace shared a 2-2 draw at Craven Cottage.
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