It was the first time he had stood on the Monaco podium in six attempts and came after two standing starts from pole position in a race halted when first lap collisions took out a fifth of the field.
McLaren's Oscar Piastri finished second, 7.1 seconds behind after 78 laps without a chance to overtake on a circuit that often produces processional races, with Ferrari's Carlos Sainz third.
Red Bull's championship leader and 2023 Monaco winner Max Verstappen started and finished sixth, only the third time in eight races this season that the triple world champion has been beaten.
Seven-times world champion Lewis Hamilton was seventh, with a bonus point for fastest lap, and Yuki Tsunoda eighth for Red Bull-owned RB.
Alex Albon scored Williams's first points of the season in ninth and Pierre Gasly took the final one for Alpine despite a first-lap collision with team mate Esteban Ocon, whose race ended immediately.
"It means a lot," said Leclerc, who screamed over the radio as he took a chequered flag waved by Kylian Mbappe while the crowd erupted and Prince Albert gave a royal thumbs up.
"It's the race that made me dream of becoming a Formula 1 driver one day."
LEAD TRIMMED
Leclerc's lights-to-flag success, and first win since the 2022 Austrian Grand Prix, trimmed Verstappen's championship lead to 31 points from 48.
Ferrari are now only 24 points behind Red Bull in the constructors' standings.
Leclerc had twice before started from pole in Monaco, in 2021 and 2022, but failed to convert the huge advantage into a top-three finish on the metal-fenced streets he has known all his life.
On a bright and sunny afternoon, and with the weight of expectation heavier than ever, he finally got to live the dream with what was only Ferrari's third win in the Mediterranean principality this century.
"Tonight is going to be a big night," he told his team on the cooling-down lap.
"No words can explain that," he added later, before Prince Albert joined in the podium celebrations by spraying his own bottle of fizz.
"It's such a difficult race; I think the fact twice I've been starting on pole position and we couldn't quite make it makes it even better in a way."
The red flags that came out after a huge crash involving Red Bull's Sergio Perez and Haas tail-enders Nico Hulkenberg and Kevin Magnussen led to a delay while fences were fixed and debris removed.
The stoppage allowed teams to change tyres - removing the need for further pitstops that might have shaken up the order - and also rescued Sainz.
The Spaniard had run wide and stopped in Casino square after a clash with Piastri left him with a puncture but he was able to return to the pits and re-start in his original grid position of third.
"It was a tight one and a very bad feeling in lap one which very quickly turned into a really good feeling after getting reinstated in P3," he said.
"I'm incredibly happy to see Charles win on his home Grand Prix," he added. "To be able to share this podium with him in P3 is great for the whole team, and it feels like we're getting stronger and stronger."
Leclerc deliberately slowed the field when the race resumed to save his tyres and prevent a big enough gap opening up behind him to allow rivals to pit for fresh and faster rubber.
