Messi scored twice and converted in a penalty shootout too, carrying his side to victory over France after the greatest final in the competition's history ended in a 3-3 draw after extra time in Qatar on Sunday.
"It's anyone's childhood dream," Messi said after hoisting the trophy.
"It's madness ... look how she (the World Cup) is, she's gorgeous. I wanted her so much. I had a vision that this would be the one ... she was getting closer."
Kylian Mbappe scored a hat-trick for France - the first treble in a men's final for 56 years - as the world's top two players shone in a wondrous duel in the Lusail Stadium near Doha.
Both men scored in the shootout too but Argentina prevailed 4-2 to lift the World Cup for the third time, with Gonzalo Montiel netting the clinching penalty to spark scenes of celebration in the stadium.
Argentina keeper Emiliano Martinez proved their hero again, saving Kingsley Coman's penalty before Aurelien Tchouameni fired wide to give Argentina their first world title since 1986.
"This is my dream," said Martinez, who also won the Golden Glove as the tournament's best goalkeeper.
"It was a game where we suffered. There could not have been a World Cup that I have dreamed of like this."
France had come from two goals down to level, with Mbappe netting twice in two minutes - first with an 80th-minute penalty and then a dazzling volley.
The France striker completed his hat-trick in the 118th minute with another spot-kick after Messi had bundled in what had looked likely to be the winner shortly before.
Earlier, Argentina had dominated, going 2-0 up in the first half with Messi, making a record-breaking 26th World Cup appearance, converting a 23rd-minute penalty.
They struck again with a sublime four-pass counter-attack, Alexis Mac Allister's cutback finding Angel Di Maria, who finished well.
In a final of extraordinary twists and turns, Mbappe became only the second man to score a hat-trick in a World Cup final following Geoff Hurst's treble for England in their 1966 victory over West Germany.
"We came back from the brink, that's what gives us so many regrets," France coach Didier Deschamps said.
But it was Messi's day as the Argentina captain, considered by many to be the greatest footballer of all-time, was at last able to lift the one trophy that had eluded him.
The diminutive No.10 is now definitively in the pantheon of soccer's greatest-ever players, alongside Pele - a record three-time World Cup champion with Brazil - and Diego Maradona, the late Argentina great with whom Messi has so often been compared.
Here, Messi achieved what Maradona did in 1986, dominating a World Cup for Argentina - even though, at 35, he was 10 years older than 'El Diego' was when shooting them to the title in Mexico.
"I wanted to close my career with this, I can no longer ask for anything else," Messi said, before adding he has no intention of hanging up his boots just yet.
"I love football and I want to continue living a few more games being world champion."
The torch will one day pass to Mbappe, whose late goals transformed the match and earned him the Golden Boot as the tournament's top scorer - but not yet.
As he waited to pick up the World Cup, Messi rubbed his hands in glee before collecting the trophy and joining his adoring teammates, for whom he has become even more of icon over the past month.
For as he lifted the biggest trophy in sport to the heavens, this was always going to be remembered as Messi's World Cup.
With Reuters, AP
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