Excitement had been brewing since the party that began after Sunday's final ahead of the players' arrival.
A private reception at a VIP suite in the airport had been arranged to greet the returning players.
"I came because of my passion for Argentina. I love Messi, I love the entire team," Alejandra Diaz, 55, a kindergarten teacher told AFP outside the airport.
Welder Javier Merina, 41, a Messi "fanatic" said he had come to the airport to try to get the star to sign a picture.
"If he doesn't I will go to Rosario, to Funes (Messi's home town) to see if I can get Messi's autograph," said Merina.
Messi, 35, finally crowned his record-breaking career with football's biggest prize as he produced one of the greatest World Cup final performances, scoring a first-half penalty and netting again in extra time.
In doing so he emulated his predecessor as Argentina's idol, Diego Maradona who inspired the country to their second world title with a series of match-winning displays at Mexico 1986.
"I remember '86 but this victory yesterday was much more emotional and much more stressful," architect Ricardo Grunfeld, 65, told AFP.
"I don't know if there's any difference with '86 but this comes at a good time," added Zulema Guereri, 80.