The players were unable to reach the city's central Obelisk monument as planned due to security concerns because of the size of the crowd - estimated by local media at four million people.
They were transferred from their parade bus to helicopters.
"The world champions are flying over the entire route in helicopters because it became impossible to continue on land due to the explosion of joy," presidential spokeswoman Gabriela Cerruti wrote on Twitter.
Television images showed people all over the city trying to catch a glimpse of their returning champions.
Argentina's players celebrate on board a bus with a sign reading "World Champions" with supporters after winning the Qatar 2022 World Cup tournament as they tour through Buenos Aires' downtown on December 20, 2022. Source: AFP / LUIS ROBAYO/AFP via Getty Images
"It is an enormous joy to see all these happy people, all together, one with the other, holding hands, giving each other hugs, kisses. We are all one today."
The team had arrived in the early hours of Tuesday at Ezeiza airport.
Despite it being 3am local time, thousands were waiting with banners, flags and flares and howling with joy after Messi and his teammates ended the country's 36-year wait to win the World Cup.
By around midday millions had congregated in downtown Buenos Aires, with major roads shut down.
The Argentine capital has been in party mode since the dramatic victory over France in Sunday's final in Qatar.
The penalty shootout victory made the country world champions for the first time since late icon Diego Maradona hoisted the trophy in 1986, and the third in total.
The government made Tuesday a national holiday to allow fans to celebrate.
Argentina's captain and forward Lionel Messi (C) holds the FIFA World Cup Trophy on board a bus as he celebrates alongside teammates and supporters after winning the Qatar 2022 World Cup tournament in Ezeiza, Buenos Aires province, Argentina on December 20, 2022. (Photo by Tomas CUESTA / AFP) (Photo by TOMAS CUESTA/AFP via Getty Images) Source: AFP / TOMAS CUESTA/AFP via Getty Images
Police were having to hold people back to allow the bus to move forward on its slow journey towards the centre of town.
But eventually they could go no further.
"They don't let us get to greet all the people who were at the Obelisco. The security agents that escorted us won't allow us to move forward," tweeted Chiqui Tapia, president of the Argentine Football Association.
"A thousand apologies on behalf of all the champion players."
