A lineup of Cuban-born baseball stars, including some of the most famous defectors in recent memory, made a triumphant return to the island Tuesday as part of the first Major League Baseball trip here since 1999. Once the object of official disdain in Cuba for leaving the country illegally, Los Angeles Dodgers outfielder Yasiel Puig, St. Louis Cardinals catcher Brayan Pena and first baseman Jose Abreu of the Chicago White Sox were swarmed by fans and members of the state media in the lobby of Havana's soaring Hotel Nacional at the start of a three-day mission meant to warm relations between MLB and Cuba. The major leagues and Cuban baseball have been moving quickly to rebuild ties since Presidents Barack Obama and Raul Castro declared a year ago Thursday that they would re-establish diplomatic relations. The official return of baseball defectors earning millions in the major leagues was a landmark in the new relationship and a dramatic manifestation of Cuba's shifting attitude toward the hundreds of players who have abandoned the country that trained them. Puig, who fled to Mexico in a smuggler's fast-boat in 2012 and then crossed the border to Texas, wrapped his childhood coach Juan Arechavaleta in a bear-hug, resting the side of his face atop the smaller man's head. "I'm very happy to be here," said Puig, who signed a seven-year, $42 million contract and was barred from returning to Cuba until he was granted special permission for this week's trip. Pena, who is from Havana, was met by at least 20 family members. They laughed at stories of the catcher's life in America and handed him the phone to talk to relatives who hadn't been able to make it to the hotel. The players will hold two days of youth clinics while league and Major League Baseball Players Association executives talk business with their Cuban counterparts, including former President Fidel Castro's son Tony, who is one of the most powerful men in Cuban baseball. League officials said they were optimistic about sealing a deal by early next year for the Tampa Bay Rays to play two spring training games in Cuba. They also hope to make progress in one day creating a legal route for Cuban players to make their way to the major leagues. "It's the goal of our commissioner and our owners to ultimately negotiate with the Cuban Baseball Federation, and with the cooperation of the US government and the Cuban government, a safe and legal path for Cuban baseball players who desire to play Major League Baseball to reach the major leagues," Dan Halem, MLB's top lawyer, told a press conference covered by what appeared to be every state newspaper, radio and television station in Cuba. Peter Bjarkman, author of the upcoming book "Cuba's Baseball Defectors: The Inside Story," said that he had counted 102 national-level players who had left Cuba this year, nearly a third of all those who have departed since 1980. The departures are part of a broader wave of Cuban emigration sparked by the fear that the US will cancel special Cold War-era privileges for Cubans as part of the new relationship with the island. US teams played spring training games in Cuba before Castro's revolution but none appeared here from March 1959 until the Baltimore Orioles faced Cuba's national team in Havana in March 1999. MLB has not returned since.