City needed victory at the Vitality Stadium to keep the title race alive, but the dropped points left Arsenal four clear at the top with only one match remaining.
The breakthrough came a day after Arsenal edged Burnley 1-0 at the Emirates Stadium to pile pressure on the defending champions.
"[I need to] congratulate Arsenal, Mikel and the backroom staff, the fans for the Premier League which they deserved," said Guardiola.
"I would love to have arrived in the last moment [and taken the title race to the last day]. Today the fatigue was there. Bournemouth had 12 days to prepare. The impact from the fresh players was not good enough. We fought a lot and we prepare next season."
At London Colney, Arsenal's squad watched City's match together through the club's official media channels before bursting into celebration at the final whistle.
Thousands of supporters gathered outside the Emirates Stadium also celebrated as confirmation of the club's first league title in 22 years arrived.
"We made history again, together. I cannot be happier, prouder for everybody that is involved in this football club. Let's enjoy the moment," Arteta stated after the City result.
The triumph marks Arsenal's 14th top-flight championship and their fourth of the Premier League era.
It is their first since the famous "Invincibles" season of 2003-04 and ends the club's longest title drought since winning their first league crown in 1931. The success also follows three successive runner-up finishes under Arteta.
Because Bournemouth held City to a draw, Arsenal will lift the trophy away from home after Sunday's final-day trip to Crystal Palace at Selhurst Park.
Arteta's side could yet make the season even more memorable when they face Paris Saint-Germain in Budapest six days later in Arsenal's first Champions League final since 2006. Arsenal have never won the competition and now stand one match away from a historic double.
Pep Guardiola has confirmed he is stepping down as manager of Manchester City after Sunday's final game of the season against Aston Villa, bringing his glittering career with the Citizens to an end.
England manager Thomas Tuchel has made a ruthless call in his first major tournament squad, leaving out several high-profile names as he named his 26-man group for the 2026 World Cup.
Arne Slot has refused to confirm whether Mohamed Salah will be involved when Liverpool host Brentford on the final day of the Premier League season, stressing that his focus remains firmly on securing Champions League qualification.
Chelsea duo Mamadou Sarr and Nicolas Jackson have both been included in the Senegal squad for the upcoming 2026 World Cup, underlining their growing importance at international level.
