The actor's death was announced by her children True and Lillie Parker on social media on Tuesday morning, Australian time.

"We are sad to inform you that our incredible, fierce and loving mother has passed away after a battle with cancer," the siblings said in a post on Twitter, Facebook and Instagram.

"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."

Alley had only been diagnosed with cancer recently, and had been undergoing treatment in Moffitt Cancer Centre.

As an actor, she starred as Rebecca Howe on Cheers from 1987 to 1993, after the departure of original star Shelley Long.

Alley also starred on the silver screen in Drop Dead Gorgeous, For Richer or Poorer, It Takes Two, Shoot to Kill and the Look Who's Talking movie franchise.

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She had her own sitcom on the network, Veronica's Closet, from 1997 to 2000.

John Travolta, who starred with Alley in the Look Who's Talking movies, made an emotional tribute to her.

"Kirstie was one of the most special relationships I've ever had. I love you Kirstie. I know we will see each other again," he said on social Instagram.

Alley's children said as iconic as she was on screen, she was an even more amazing mother and grandmother.

"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," they said.