Ted Danson and Cheers Cast Mourn Kirstie Alley: 'So Grateful for All the Times She Made Me Laugh'

Ted Danson and members from the cast of Cheers are mourning former costar Kirstie Alley, who died of cancer on Monday at age 71, her children confirmed to PEOPLE.

"I was on a plane today and did something I rarely do," Danson said in a statement to PEOPLE. "I watched an old episode of Cheers."

"It was the episode where Tom Berenger proposes to Kirstie, who keeps saying no, even though she desperately wants to say yes," the actor continued. "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."

RELATED: Kelsey Grammer, Jamie Lee Curtis and Other Stars React to Kirstie Alley's Death: 'You Were One of a Kind'

Alley rose to fame in 1987 when she starred as Rebecca Howe on NBC's Cheers. She earned a Golden Globe for best actress and an Emmy for outstanding lead actress for her part in the Boston-based series in 1991.

Danson recalled his time playing opposite Alley. "She made me laugh 30 years ago when she shot that scene, and she made me laugh today just as hard," he shared.

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"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," he concluded.

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RELATED: Kirstie Alley Dead: Star of 'Cheers' Dies at 71 After Short Battle with Cancer

In a statement to PEOPLE, Alley's Cheers costar Kelsey Grammer also shared his thoughts: "I always believed grief for a public figure is a private matter, but I will say I loved her."

Rhea Perlman, another of Alley's costars from Cheers, shared a statement with PEOPLE.

"Kirstie was a unique and wonderful person and friend," she said. "Her joy of being was boundless. We became friends almost instantly when she joined the cast of Cheers. She loved kids and my kids loved her too. We had sleepovers at her house, with treasure hunts that she created."

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Perlman continued: "She had massive Halloween and Easter parties, and invited the entire crew of the show, and their families. She wanted everyone to feel included. She loved her children deeply. I've never met anyone remotely like her. I feel so thankful to have known her. I'm going to miss her very, very much."

RELATED: John Travolta Remembers Kirstie Alley After Her Death: 'One of the Most Special Relationships'

Alley went on to receive her second Emmy win for her portrayal of Sally Goodson in David's Mother in 1994.

Alley also appeared on television shows including Veronica's Closet, Fat Actress, Kirstie and Scream Queens, and on the big screen in Star Trek II: The Wrath of Khan (1982), Summer School (1987), Look Who's Talking (1989), It Takes Two (1995) and Drop Dead Gorgeous (1999).

NBCU Photo Bank/NBCUniversal/Getty Ted Danson and Kirstie Alley on Cheers

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In 2010, her life was chronicled on the A&E reality TV series Kirstie Alley's Big Life. She also competed on season 12 of Dancing with the Stars and season 7 of The Masked Singer.

Alley's children, True and Lillie Parker, announced the actress had died from cancer. In a statement to PEOPLE, True and Lillie confirmed that Alley died on Monday.

RELATED: Remembering Kirstie Alley's Life in Photos

"We are sad to inform you that our incredible, fierce and loving mother has passed away after a battle with cancer, only recently discovered," they said in a statement.

"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," they continued. "As iconic as she was on screen, she was an even more amazing mother and grandmother."

As news of her death circulated, many stars shared tributes for Alley to PEOPLE and on social media.