Spanish midfielder Rodri scored the only goal of the game at the Ataturk Stadium in Turkey with a well guided strike in the 68th minute.
Manchester City thus complete the treble this season, joining Manchester United as the only English sides to win the FA Cup, Premier League and Champions League in the same season.
City manager Pep Guardiola has won his third Champions League title and his first since 2011 with Barcelona.
It was a scrappy game in which City were not at their usual fluid best but it was the result that mattered to the English champions especially after coming so close in recent seasons.
Erling Haaland, so subdued by a resolute Inter Milan defence shot straight at Andre Onana in the first half and City had scares of their own in the second period as Federico Di Marco headed against the crossbar and substitute Romelu Lukaku placed a header straight at Ederson late on.
At the end of it all, the sight of captain Ilkay Gundogan lifting the trophy was what City craved and they can finally count themselves among Europe's elite with their first continental triumph.
