"Fidel Castro is dead!" Trump tweeted on the news of the 90-year-old's death.
The longtime revolutionary leader died Friday, presenting potential opportunities for change in a country whose relations with the United States have recently begun to improve.
Castro's death came just weeks after Trump, a frequent critic of the reopening of diplomatic ties with Cuba, was elected president.
"Today, the world marks the passing of a brutal dictator who oppressed his own people for nearly six decades," Trump said in a statement issued a couple of hours after his tweet.
"Fidel Castro's legacy is one of firing squads, theft, unimaginable suffering, poverty and the denial of fundamental human rights. While Cuba remains a totalitarian island, it is my hope that today marks a move away from the horrors endured for too long, and toward a future in which the wonderful Cuban people finally live in the freedom they so richly deserve."
The President-elect added, "Though the tragedies, deaths and pain caused by Fidel Castro cannot be erased, our administration will do all it can to ensure the Cuban people can finally begin their journey toward prosperity and liberty. I join the many Cuban-Americans who supported me so greatly in the presidential campaign, including the Brigade 2506 Veterans Association that endorsed me, with the hope of one day soon seeing a free Cuba."
Vice President-elect Mike Pence tweeted of the dawning of new hope now that "the tyrant" has died.
"The tyrant #Castro is dead. New hope dawns. We will stand with the oppressed Cuban people for a free and democratic Cuba. Viva Cuba Libre!" Pence said.
Trump had threatened to undo efforts by President Barack Obama to bring the US and Cuba closer together, slamming the recent agreement between the two countries for better relations.
In October, Trump criticized the Obama administration's effort to normalize relations with Cuba as a "very weak agreement," although he said some sort of a deal is "fine."
Trump told Miami CBS journalist Jim DeFede that he would do "whatever you have to do to get a strong agreement," even if that meant breaking off the recently resumed diplomatic contacts.
In March, the billionaire businessman had expressed interest in opening a hotel in Cuba, telling CNN it was "OK to bring Cuba back into the fold."
The real estate developer also had promised during the campaign "to find out" if a Newsweek report that his associates may have violated the US-Cuban embargo in 1998 by going to Cuba to explore business opportunities was true. A Bloomberg story said additional Trump associates went to Cuba in 2012 and 2013 to entertain opening a golf resort.
"I don't know exactly where they were. I can tell you that Cuba wants to, you know, really negotiate with us. They've said, 'We want to negotiate.' They want to make some kind of a deal. I've said, I don't want to make any deals unless we know we have a deal with Cuba," he told DeFede.
"But you think they did, in fact, go to Cuba?" DeFede asked.
"Well, know that Cuba wants us to go there. I'm not interested in going," Trump replied.
DeFede countered, "No, I meant as emissaries -- did those individuals travel there to have those discussions?"
"I would have to find out," Trump said. "I know they had some meetings, but I would have to find out."