Cheering fans, many wrapped in Argentine flags, partied around the city's iconic Obelisk in the early hours of the morning despite the low temperatures of the southern hemisphere winter.
The party ended abruptly after more than four hours when police deployed water trucks and officers to clear the streets, causing a rush of people.
Some hurled stones at the police but many quickly dispersed in the face of advancing riot police.
The authorities reported no arrests or injuries.
"We are champions of America, let's enjoy this precious moment that is unique for us since we have the chance to celebrate with the greatest who is ...Messi and the farewell of 'Fideo' (Angel) Di Maria," a chanting Pablo Inigo told AFP.
President Javier Milei congratulated the two-time America's champions posting "Let's go Argentina carajo..!!!!! We are champions again...!!!!" on social platform X.
The win was the Argentine's third straight major tournament title following their 2021 Copa victory and triumph in the 2022 World Cup in Qatar.
Several hundred people had gathered at the site to follow the game but it was not broadcast on the screens, and they had to settle for watching it on their phones.
Others crowded the surrounding bars and cafes huddling around TV sets.
Celebrations were also marred by the death of a fan who, before the match, started climbed a structure in front of the Obelisk to wave a flag but lost his balance and fell six meters.
Firefighters removed the body of the 29-year-old victim.
