Trump tweeted and exclamation tweet.
"Fidel Castro is dead!"
He further called Castro a brutal dictator. Mr Trump, who takes office in January, said he hoped Cubans could move towards a freer future.
Castro came to power in 1959 and ushered in a Communist revolution. He defied the US for decades, surviving many assassination plots.
Supporters said he returned Cuba to the people. Critics called him a dictator.