A second consecutive defeat for the Gunners left Mikel Arteta’s men still four points adrift of City with one game left for them to play.
Taiwo Awoniyi’s winning goal also had huge ramifications at the bottom of the table as Forest are now safe from relegation in their first season back in the top flight for 23 years.
City’s title triumph could be the start of a treble as Pep Guardiola’s men face Manchester United in the FA Cup final and Inter Milan in the Champions League final next month.
Arsenal pushed the defending champions most of the way but crumbled in the decisive final months of the season.
They have won just two of their last eight games to allow City to canter over the line with three games to spare.
The visitors rarely even looked like scoring as a raucous atmosphere at the City Ground roared Forest onto survival.
Arteta’s decision to name an experimental back four without any recognised full-backs backfired inside the first 20 minutes.
Morgan Gibbs-White has been central to Forest’s recovery after winning just one of their opening 11 league games.
The England under-21 international created the only goal as he teed up Awoniyi to dink home his fifth goal in three games over Aaron Ramsdale.
Forest were then happy to retreat and defend their lead, but Arsenal were a shadow of the vibrant young side that shone in the early months of the season.
Bukayo Saka’s tame shot that was easily saved by Keylor Navas was the closest they came to an equaliser.
Arteta’s squad is the second youngest in the Premier League and they have run out of steam just as City have hit top speed.
The newly-crowned champions are unbeaten in 23 games in all competitions, including a 4-1 thrashing of Arsenal when the sides met in a top-of-the-table clash last month.
At the other end of the table, Forest move six points clear of the drop zone meaning two from Everton, Leeds or Leicester will join Southampton in the Championship next season.