Uruguay and Argentina had already said they will officially launch their joint proposal at a ceremony involving the country’s two leaders in October.
Uruguay hosted the inaugural World Cup in 1930 and is hoping to win the rights to the tournament along with its neighbors to mark the centenary of the event.
“I can confirm that the presidents of Paraguay, Argentina and Uruguay have agreed to be (joint) candidates for the 2030 World Cup,” Cartes said on Twitter.
Separately the head of South American football confederation CONMEBOL, Alejandro Dominguez, tweeted that he was meeting with Cartes to plan Paraguay’s part in the bid.
Paraguayan government sources said the countries were planning to propose six venues for the tournament in Argentina and three each in Uruguay and Paraguay.
The presidents of each of the three soccer-mad countries are former football executives.
South America last staged the World Cup in Brazil in 2014. Any bid for 2030 is likely to face stiff competition from the Asia region, where China is expected to be the front-runner to stage the finals.
The next World Cup takes place in Russia, with Qatar staging the event in 2022.
A joint United States-Mexico-Canada bid is the favorite to win the 2026 tournament, with only one other country, Morocco, so far expressing an interest in entering the bidding race.
The Paraguayan capital Asuncion was rocked by deadly riots against Cartes in April but calm was restored within days.
The unrest forced Cartes to back down from efforts to change the constitution in order to seek re-election next year.
“Paraguay is destined for great things and we are prepared to receive the biggest football festival on its centenary,” Cartes said on Thursday.