The players are expected to spend a few hours at the Argentine Football Association (AFA) facilities near the airport before heading at noon to the huge Obeliso monument in the center of town, where hundreds of thousands are likely to gather.
Argentina beat France 4-2 on penalties after a scintilaing 3-3 draw, with Messi scoring twice France's Kylian Mbappe netting three times. Messi, 35, announced that the final would be his last match in the World Cup though he intends to play a few more games for the national side.
A picture of Messi was emblazoned on the plane's tail with the words: "one team, one country, one dream" on its side.
The players made their way from the plane along a red carpet straight to a white open-top bus with the words "world champions" and three stars on its side as their World Cup theme song "Muchachos" by ska band La Mosca blared out.
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.
Argentina had led 2-0 with 10 minutes of normal time left and 3-2 with only two minutes of extra-time to go but Kylian Mbappe completed only the second World Cup final hat-trick in history to take the gripping final to penalties, before Gonzalo Montiel swept home the decisive spot kick.
Despite the huge numbers of revelers during Sunday's festivities "people acted in a very positive way," a spokesperson for the municipality said.
Fewer than 20 people were arrested for isolated incidents of violence or theft.
