Local media estimated that there were already more than 100,000 people waiting for the players at the iconic Obelisk pillar by mid-morning, with more crowds joining from streets on all sides.
The Argentine capital has been in party mode since their dramatic victory over France in Sunday's (December 18) final in Qatar, which gave the country its first World Cup win since Diego Maradona hoisted the trophy 36 years ago.
The players are expected to spend a few hours at the Argentine Football Association facilities near the airport before heading at noon to the huge Obelisk monument in the centre of town.
Argentina beat France 4-2 on penalties after a scintillating 3-3 draw, with Messi scoring twice and France's Kylian Mbappe netting three times.
Messi, 35, said the final would be his last match in the World Cup, though he intends to play a few more games for the national side.