Liotta, whose blistering turn as real-life mobster Henry Hill in Scorsese's crime masterpiece won universal admiration, was shooting a new film in the country when he died in his sleep.
Police said emergency services were called early Thursday morning to a hotel in Santo Domingo where they found Liotta already dead.
The actor's publicist in Los Angeles, Jennifer Allen, confirmed his death, saying there were no suspicious circumstances.
Allen said he had been working on a movie called "Dangerous Waters."
Liotta became a household name in 1990 when he was cast alongside Robert De Niro and Joe Pesci in what is widely considered one of the greatest films of the 20th century.
"Goodfellas" won one Oscar, and was nominated for five others. Scenes from the movie continue to resonate as cultural touchstones more than three decades later.
A year before "Goodfellas," Liotta had played baseball star "Shoeless Joe" Jackson in beloved sports movie "Field of Dreams," opposite Kevin Costner.
The film was nominated for three Oscars, including best picture.
'A gentle man'
News of Liotta's death sparked a flood of tributes from colleagues and contemporaries, with "Goodfellas" co-star Lorraine Bracco, who played on-screen wife Karen, saying she was "utterly shattered to hear this terrible news."
"I can be anywhere in the world & people will come up & tell me their favorite movie is Goodfellas," she tweeted.
"Then they always ask what was the best part of making that movie. My response has always been the same... Ray Liotta."
Actress Jamie Lee Curtis, who worked with Liotta on "Dominick and Eugene," tweeted: "His work as an actor showed his complexity as a human being. A gentle man. So sad to hear."
Jennifer Lopez, who starred opposite Liotta in the television series "Shades of Blue," said he was "the epitome of a tough guy who was all mushy on the inside."
"Like a raw nerve, he was so accessible and so in touch in his acting. We lost a great today ... RIP RAY ... it's so sad to lose you what seems way to soon."
Seth Rogen, who was cast alongside Liotta in black comedy "Observe and Report" called him "a true legend of immense skill and grace... a lovely, talented and hilarious person."
Despite branching out to show the breadth of his talent, Liotta had recently returned to the world of mob films, with roles in Steven Soderbergh's "No Sudden Move" and 2021's "The Many Saints of Newark."
Alessandro Nivola, who played alongside Liotta in "The Many Saints of Newark," a prequel to hit TV series "The Sopranos," said his co-star's death had come "too soon."
"I feel so lucky to have squared off against this legend in one of his final roles," he wrote on Twitter.
"The scenes we did together were among the all time highlights of my acting career. He was dangerous, unpredictable, hilarious, and generous with his praise for other actors."
Liotta was born in Newark, New Jersey, in December 1954.
Variety reported he was left at an orphanage at birth and adopted when he was six months old.
At the University of Miami, he performed in musicals, and after graduating landed a role on a soap opera that would provide him with three years' work to 1981.
His first movie came in 1983, but it wasn't until 1986's "Something Wild" opposite Melanie Griffith and Jeff Daniels that he came to wider attention.
The comedy-action-romance was screened at Cannes and scored Liotta a Golden Globe nomination for supporting actor.