Amid reports manager Pep Guardiola will step down at the end of the season, City needed to win at Vitality Stadium on Tuesday (Wednesday AEST) to take the title race to the final day.
Erling Haaland equalised in added time to cancel out Junior Kroupi's record-breaking 13th top-flight goal of the campaign, but the visitors were unable to force a winner as Guardiola, who had Arteta as his assistant for two of City's six Premier League titles, was denied a potential fairytale farewell.
"We were close. On behalf of everyone at Manchester City, we congratulate Mikel and all the staff, players and fans on winning the Premier League," 55-year-old Guardiola told Sky Sports.
"They deserve it, for so much hard work and effort.
"Next season, we will be back."
Bournemouth's historic achievement was a fitting way to mark the final home game of head coach Andoni Iraola, who was given a rousing send-off at fulltime ahead of being replaced by Marco Rose in the summer.
Following a remarkable 17th league game without loss, the Cherries are guaranteed a top-seven finish and remain in contention for Champions League football ahead of Sunday's season finale at Nottingham Forest.
City are now an insurmountable four points adrift of the table-topping Gunners, with speculation Guardiola is set to end his contract a year early and be succeeded by Enzo Maresca after the weekend visit of Aston Villa.
The 10-time English champions arrived on the south coast three days after lifting the FA Cup but with news of Guardiola's possible departure dominating the headlines.
Travelling fans chanted "one more year, one more year, Guardiola", before Kroupi raised the roof with a stunning 39th-minute opener.
After being released by Marcus Tavernier, Adrien Truffert cut the ball back from the left and 19-year-old forward Kroupi curled a stunning finish into the right corner before celebrating becoming the outright highest scoring teenager in a debut Premier League season, with a somersault.
Bournemouth's Rayan and David Brooks both hit the post before Haaland swept home in the fourth minute of added time to jangle the nerves of watching Arsenal fans.
But the home side held on sparking wild celebrations around the Gunners' home ground in London.
Arteta's players can now stand alongside club icons Thierry Henry, Dennis Bergkamp and Ian Wright, who previously led the club to the summit of English soccer. And Arsenal's current class could yet break new ground by winning the Champions League for the first time against defending champion Paris Saint-Germain.
Tottenham's fight to avoid relegation will go to the final day of the season after they were beaten 2-1 by Chelsea at Stamford Bridge to hand 18th-placed West Ham United a lifeline.
A point would have put an end to Spurs' nightmare that still threatens to pull them into the second tier for the first time in 48 years, but Enzo Fernandez and Andrey Santos scored in each half for the Blues.
Richarlison got one back 16 minutes from the end to offer Roberto De Zerbi's side late, but fruitless, hope.
