The Belo Horizonte club, twice winners of the Brazilian championship and the Copa Libertadores, said they would spend a week training in Orlando before hopefully ending the trip with at least one friendly match against a U.S. club.
Brazilian champions Fluminense and promoted Atletico Paranaense said last month they would send teams to the United States and Europe respectively.
The teams can travel because the Brazilian season will pause for two weeks in June as the country hosts the Confederations Cup, the test run for next year's World Cup. The Confederations Cup is being held in six cities between June 15-30.
Cruzeiro said the trip had the twin benefit of freeing up their highly rated training complex to be used by one of the eight teams participating in the tournament.
Decades ago, big Brazilian clubs regularly spent weeks during the European summer playing friendlies, tournaments and challenge matches but they stopped long ago because the Brazilian calendar no longer permits them.
The Botafogo side led by Garrincha played 18 games in Europe in just two months in 1955 and in 1956 went to 45 cities and faced six national sides, including England and Italy.
In the 1960s, Pele's Santos withdrew from the Copa Libertadores in order to go on more lucrative foreign tours.
Many clubs now complain that the Brazilian season, which starts in late January with state tournaments and ends with the May-December national championship, does not allow them to travel abroad and so they are grabbing the chance this year.
"The advantage of this is that we can get international experience," said Luiz Greco, Atletico Paranaense's director of international relations.
"Coming up against new players and different styles makes us better players and the players learn a new culture, as well."
Santos's president has lobbied hard for Brazil to coordinate its season with Europe to allow Brazilian sides to travel to the old world. Brazilian clubs need to not only test themselves against the best of Europe but also make commercial inroads, particularly in Asia, said Luis Alvaro de Oliveira Ribeiro.
"The European clubs already have a presence in these places and every season they increase their share in the world market," he said.
Brazilian clubs are more professionally run today than they were a few years ago but they still have little commercial presence outside Brazil. No Brazilian teams feature on Deloitte's annual Football Money League list of the 20 richest clubs.
Cruzeiro's decision to travel follows a similar one by Fluminense.
Under a deal with U.S. club Orlando City, Fluminense will spend a week in Florida. The Brazilians will train at the club's headquarters before ending the trip with a friendly against their hosts at the 70,000-seat Citrus Bowl.
Atletico Paranaense will play two tournaments in Europe at the end of May, facing teams such as Hertha Berlin and VfL Bochum in the Yokohama Cup in Germany and Queens Park Rangers and Feyenoord in the Esad Osmanovski Cup in the Netherlands.
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- Atletico Paranaense