Kirstie Alley, the TV and film star known for her roles in Cheers, Veronica’s Closet and Look Who’s Talking, has died at the age of 71.

Alley’s death was confirmed on Monday night in a statement from her children, William “True” Stevenson and Lillie Price Stevenson, which was posted to her social media account. Her manager also separately confirmed her death.

Alley had recently been diagnosed with cancer, and was being treated at the Moffitt Cancer Center in Florida, her family revealed.

“To all our friends, far and wide around the world … We are sad to inform you that our incredible, fierce and loving mother has passed away after a battle with cancer, only recently discovered,” the statement said. “She was surrounded by her closest family and fought with great strength, leaving us with a certainty of her never-ending joy of living and whatever adventures lie ahead. As iconic as she was on screen, she was an even more amazing mother and grandmother.”

“We are grateful to the incredible team of doctors and nurses at the Moffitt Cancer Center for their care. Our mother’s zest and passion for life, her children, grandchildren and her many animals, not to mention her eternal joy of creating, were unparalleled and leave us inspired to live life to the fullest just as she did. We thank you for your love and prayers and ask that you respect our privacy at this difficult time.”

Alley’s ex-husband, actor Parker Stevenson, wrote: “I am so grateful for our years together, and for the two incredibly beautiful children and now grandchildren that we have. You will be missed.”

“I was on a plane today and did something I rarely do. I watched an old episode of Cheers,” Ted Danson, who played Sam Malone opposite Alley in Cheers, told Deadline. “It was the episode where Tom Berenger proposes to Kirstie, who keeps saying no, even though she desperately wants to say yes. Kirstie was truly brilliant in it. Her ability to play a woman on the verge of a nervous breakdown was both moving and hysterically funny. She made me laugh 30 years ago when she shot that scene, and she made me laugh today just as hard. As I got off the plane, I heard that Kirstie had died. I am so sad and so grateful for all the times she made me laugh. I send my love to her children. As they well know, their mother had a heart of gold. I will miss her.”

Kelsey Grammer, who played Frasier Crane on Cheers, said, “I always believed grief for a public figure is a private matter, but I will say I loved her.”

John Travolta, Alley’s co-star in Look Who’s Talking, also paid tribute. “Kirstie was one of the most special relationships I’ve ever had. I love you Kirstie,” he wrote. “I know we will see each other again.”

Born in Kansas in 1951, Alley’s breakout arrived in 1987 when she joined the cast of the sitcom Cheers, playing the bar’s new manager Rebecca Howe. Alley was cast after Shelley Long decided to leave the show, leaving the creators Glen and Les Charles scrambling to find a new female lead. Wanting to find an unknown, the Charles brothers finally cast Alley after Carl Reiner personally vouched for her comedy skills, having directed her in 1987 film Summer School. Alley would win a Golden Globe and an Emmy for her performance in the show.

She won a second Emmy in 1994 for her performance as a mother of an autistic child in the made-for-television film David’s Mother.

Throughout the 1980s and 1990s, Alley appeared in films including Star Trek II: The Wrath of Khan, Summer School, Drop Dead Gorgeous, Woody Allen’s Deconstructing Harry, and Look Who’s Talking and Look Who’s Talking Too. In television, she mainly played comedic roles after Cheers, including the titular character in Veronica’s Closet, the short-lived sitcom Kirstie, and the horror-comedy anthology series Scream Queens.

In the early 2000s, amid extensive coverage of her weight in gossip outlets, Alley created and starred in the show Fat Actress, playing a fictionalised version of herself, as a fat actor trying to find success in Hollywood while fending off predatory tabloids and attempting to find love.

Later in life, Alley went into reality television, documenting her efforts to lose 75 pounds (34kg) in the reality show Kirstie Alley’s Big Life, and competing on Dancing with the Stars, the UK’s Celebrity Big Brother and The Masked Singer.

In 1970, Alley married her high-school sweetheart Bob Alley, who had the same name as her father; they divorced in 1977. In 1983, she married Stevenson and they adopted their two children. They divorced in 1997.

Alley became a Scientologist in 1979 while struggling with a cocaine addiction, later crediting the church’s drug treatment program for her sobriety.

A vocal supporter of former US president Donald Trump since 2016, Alley claimed she had been “blackballed” in Hollywood due to her politics, saying: “You can be cooking meth and sleeping with hookers, but as long as, apparently, you didn’t vote for Trump ... I feel like I’m in The Twilight Zone a bit.”

Her Scream Queens co-star Jamie Lee Curtis called her “a great comic foil” and “a beautiful mama bear”. “We agreed to disagree about some things but had a mutual respect and connection,” she added. “Sad news.”