The presidents of the three nations met on Wednesday and revealed their plans in a media conference in Argentina's capital city, Buenos Aires.
The bidding process is not set to begin until 2021, but Argentina, Uruguay and Paraguay are expressing themselves early in what is sure to be a well-contested race.
Uruguay hosted - and won - the very first World Cup in 1930, and their participation as joint hosts 100 years later could add extra romance to the tournament's build-up.
Paraguayan president Horacio Cartes honed in on that point during Wednesday's media conference.
He said: "We know there are other countries that want it but I think the 100-year anniversary of the first World Cup in Uruguay makes the region a very attractive prospect."
Cartes' Argentinian counterpart Mauricio Macri revealed that Uruguay conceived the initial idea for a joint bid, and it did not take long for his country to say "yes" to them or Paraguay.
"The original idea came from Uruguay and it took us 40 seconds to say yes," Macri added.
"And when Paraguay was proposed it took me another 40 seconds to agree. Uruguay was also very positive about their inclusion and I think that gives the candidacy more power."
While Uruguay and Argentina (1978) have both hosted the competition before, it would be a historic first for Paraguay, who did not qualify for any of the last three World Cups on South American soil.