The U.S. Treasury Department issued a license Friday allowing the Cubans to participate in the 16-team tournament.
Baseball's first application was denied in mid-December by the Treasury Department's Office of Foreign Assets Control, but the commissioner's office and the players' association reapplied after Cuba said it would donate any profits it receives to victims of Hurricane Katrina.
Major League Baseball wants the Cubans to take part, to make this new "World Baseball Classic" as competitive as possible, reports CBS News correspondent Dan Raviv.
U.S. laws aimed at punishing Fidel Castro's communist government prohibit certain commercial transactions with Cuba, generally attempting to deny money.
"Working closely with World Baseball Inc. and the State Department, we were able to reach a licensable agreement that upholds both the legal scope and the spirit of the sanctions," Treasury spokeswoman Molly Millerwise said.
"This agreement ensures that no funding will make its way into the hands of the Castro regime. The Treasury is pleased to now be able to issue this license and looks forward to seeing all of the teams showcase their talents on the international stage."
After the initial rejection, the International Baseball Federation threatened to withdraw its sanction of the tournament if Cuba was not allowed to participate. In addition, Puerto Rico threatened to withdraw as a host.
"We were always positive," said Antonio Munoz, the promoter who paid millions of dollars to stage the first two rounds in Puerto Rico. "There were some negative people, but they were wrong in the end."
Initial reaction among Cuban fans was positive.
"Oh, magnificent! Tremendous!" exclaimed Osvaldo Herrera, who was standing on a street corner in Havana with three other sports lovers discussing Cuban baseball.
The tournament, the first in which the world's top players will participate on national teams, runs from March 3-20. The other 15 teams submitted their 60-man preliminary rosters earlier this week.
Cuba won the Olympic gold medal in 1992, 1996 and 2004, and the United States won in 2000. Olympic baseball was initially limited to amateur players, but even after professionals were allowed in for the 2000 Sydney Games, major leaguers didn't participate because baseball doesn't stop its regular season for the Olympics.
Barry Bonds, Alex Rodriguez and Roger Clemens are among the big-name players on the U.S. roster, and Manny Ramirez, Albert Pujols and Vladimir Guerrero are on the Dominican team. Puerto Rico and Japan also are expected to be among the top teams at the tournament.