Pre-match talk of a stroll to European soccer's most-cherished crown proved off the mark, however, and it took a Rodri goal after 68 minutes to crack Inter's resistance.
Even then City's massed ranks had their heads in their hands as Inter threatened to drag a cagey final into extra time with goalkeeper Ederson making two superb late saves.
An eruption of joy greeted the final whistle with City's players sprinting towards their fans in the Ataturk Stadium.
"You have to be lucky ... It was written in the stars. It belongs to us," said City manager Pep Guardiola. "With this competition, the treble is so difficult."
City not only won their first European trophy since claiming the now-defunct European Cup Winners' Cup in 1970, they also became only the second English team to win a treble of Premier League, FA Cup and Champions League, matching Manchester United's sweep in 1999 when City were in the third-tier.
Inter, bidding to lift the trophy for a fourth time, stifled Guardiola's side with a superbly-executed game plan in the first half in which City's Kevin De Bruyne went off injured.
City may have experienced a horrible sense of deja-vu as chief playmaker De Bruyne also failed to finish the final two years ago when City fell short against Chelsea.
Even City's Norwegian goal-machine Erling Haaland found himself shackled, but in the end Spanish midfielder Rodri, starting his 52nd game of the season, came to the rescue.
"Emotional. A dream come true. All these guys around here waited I don't know how many years. They deserve, we deserve," Rodri told BT Sport as Guardiola hugged his players and City's fans sang the name of Sheikh Mansour, whose takeover of the club in 2008 has turned City into serial trophy-winners.
"It wasn't easy. What a team we faced, the way they defend and counter-attack. Finals are like this. Emotions and nerves are there. We competed like animals."
City have now won 17 trophies since the 2008 takeover, although there is a cloud on the horizon with the club faced with 100 charges of alleged breaches of Premier League financial regulations dating back to 2009.
On Saturday alongside the Bosphorous, that was the last thing City's joyous fans cared about as they serenaded their side with club anthem Blue Moon a collection of hits by Oasis, whose brothers Noel and Liam Gallagher are staunch fan.
In finally guiding City to the European Holy Grail after some gut-wrenching near misses, Guardiola became the first manager to achieve two trebles in European football, having done the Spanish equivalent with Barcelona in 2009.
He has delivered 12 major trophies for City since 2016 and, with the Champions League jinx broken, any sense of inferiority they may have felt to established European royalty like Real Madrid, Bayern Munich and Liverpool has been swept away.
"We want more," Rodri warned.
Players deliver
Guardiola's side fluffed their lines in Porto two years ago against Chelsea. This time Guardiola and his players delivered, although it was never going to be straightforward.
Simone Inzaghi's side disrupted City's rhythm in the first half with their back three of Matteo Darmian, Francesco Acerbi, Alessandro Bastoni superb behind a tireless midfield guard.
Haaland had two efforts, the second saved superbly by Andre Onana, but Guardiola looked anxious on the touchline -- and even more so when De Bruyne was forced off in the 36th minute.City were unusually sloppy after the break with passes going astray, with one from Manuel Akanji playing in Lautaro Martinez who selfishly failed to pick out substitute Romelu Lukaku.
Inter's fans grew increasingly vocal while City's were virtually silent at the other end but all that changed when Bernardo Silva found some space in the blue and black wall and his cut back was dispatched by Rodri.
To their credit, Inter responded immediately and came agonizingly close to an equalizer when Federico Dimarco looped a header against the bar with Ederson beaten and then saw his follow-up header hit Lukaku, who had replaced Edin Dzeko.
Lukaku went even closer near the end when his point-blank header was somehow kept out by Ederson who then made another save from Francesco Acerbi. It was City's night.