The President said it was hard to think of a policy "that makes less sense than the prior administration's awful and misguided deal" with the "brutal" Castro government.
The audience in Miami cheered enthusiastically, and chanted the president's name, while individuals shouted "Viva Trump!".
Trump told the crowd that enforcing the ban on tourism and the embargo would continue to be priorities.
Cuba's government on Friday criticized Donald Trump's "hostile rhetoric" in announcing new restrictions on U.S. ties to the island nation, but reiterated Havana's willingness to hold "respectful dialogue" with Washington.
He isn't though, reversing key diplomatic and commercial ties. Yet island officials say they remain willing to continue "respectful dialogue" on topics of mutual interest.
Trump aides say Obama's efforts amounted to "appeasement" and have done nothing to advance political freedoms in Cuba, while benefiting the Cuban government financially.More news: Trump tweets about Clinton after news of obstruction of justice investigation
Trump will announce his new approach early Friday afternoon at the Manuel Artime Theater in Miami's Little Havana, the heart of America's largest Cuban-American community, whose support aides believe helped him win Florida in the election. "They are rejected officially today - rejected".
"Effective immediately, I am cancelling the last administration's completely one-sided deal with Cuba", Trump declared as he made a full-throated verbal assault on the government of Cuban President Raul Castro. In practice, however, many recent changes to boost ties to Cuba will stay as they are.
Trump's measures stop short of reversing Obama's opening, but they signal a tougher stance that could slow the number of Americans who have begun to head to Cuba for Havana vacations and beach holidays.
Cubans said they were crestfallen to be returning to an era of frostier relations with the United States as the news spread that U.S. President Donald Trump was set to revert parts of the historic detente with Cuba, Reuters reported.
U.S. citizens will still be able to take commercial flights to Cuba, but only for 12 specific reasons - ranging from journalism to educational activities - which will be more tightly enforced.
Without doubt it will impact those in the tourism industry that have benefited from a threefold increase in US visits in the last two years, although it is unclear just how much.
Embassies in Havana and Washington will remain open.More news: Britain 'should stress jobs and prosperity in #Brexit talks': Hammond
Cruises and flights from the USA to Cuba will continue, according to CNN, but tourists will be restricted from entering Cuba.
He added that US sanctions would not be lifted until Cuba frees "political prisoners" and holds "free elections".
As to travels, individual leisure travel, permitted by the Obama administration, will be prohibited, and Americans will be required to visit Cuba through tour groups. The changes would make it more hard for traveler and eventually could make traveling to Cuba more hard for passengers, who would be subject to audit by the Treasury Department to ensure their trips to Cuba fall into one of the 12 acceptable purposes.
The changes will not go into effect until new documents laying out details are issued. "President Trump's policy changes will encourage American commerce with free Cuban businesses and pressure the Cuban government to allow the Cuban people to expand the private sector". "You heard that pledge. and here I am", he said in Florida.
Cheered by Cuba hardliners in both parties, Mr Trump's new policy is broadly opposed by U.S. businesses eager to invest in Cuba.
"He used rhetoric that President Obama had left behind so it definitely feels like an enormous setback in relations". The rules also require a daylong schedule of activities created to expose the travelers to ordinary Cubans.
The Obama policy is likely to be revised rather than reversed entirely. "This will be the first time in several decades that the Cuban people will have an economic advantage over the Cuban military". "We know what is going on and we remember what happened".More news: Tapwrit Wins the Belmont Stakes
For Cubans, the shift risks stifling a nascent middle class that has started to rise as Americans have flocked to the island on airlines, patronizing thousands of private bed-and-breakfasts.
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