Williams' children, Zak and Emily Hudson, released a statement to PEOPLE through their family spokeswoman Liza Cranis on Monday, stating that their mother died peacefully last Wednesday following a brief illness.
"The passing of our kind, hilarious mother, Cindy Williams, has brought us insurmountable sadness that could never truly be expressed," read the statement. "Knowing and loving her has been our joy and privilege. She was one of a kind, beautiful, generous and possessed a brilliant sense of humor and a glittering spirit that everyone loved."
Christopher Ameruoso Cindy Williams
"We have always been, and will remain, SO proud of her for many things… her lifelong mission to rescue animals, her prolific artistry, her faith, and most of all, her ability to make the world laugh!" they continued.
"May that laughter continue in everyone, because she would want that. Thank you for loving our Mom, she loved you too."
Silver Screen Collection/Getty Penny Marshall and Cindy Williams on Laverne & Shirley
Williams was best known for her role on Laverne & Shirley, which ran from 1976 to 1983 and was one of ABC's most popular sitcoms at the time.
The series was born out of an episode of Happy Days in 1975, in which Williams portrayed Shirley and Penny Marshall played Laverne DeFazio. Their characters were so popular, ABC hired the two for their own spin-off show, which debuted on the air the following year.
The show focused on Laverne and Shirley, two roommates that struggled to make ends meet while trying to find Mr. Right.
The pair were one of the best-known duos on television, but the costars also formed a close bond that extended beyond the cameras — and they often spoke about that special connection.
Marshall even spoke so highly of Williams as to place her as the more talented one in their famed collaboration: "[Williams] is a better actress than me. Trust me," she said. "She has a better range. She can [memorize] a paragraph. I can't do an accent."
Marshall preceded Williams in death, having died in December 2018, also at the age of 75.
Besides Laverne & Shirley, Williams also was well-known for film roles such as George Lucas' 1973 American Graffiti and Francis Ford Coppola's The Conversation from 1974.
Born in Van Nuys, Calif. in 1947, Williams first became interested in acting in high school. After graduation she attended L.A. City College where she majored in Theatre Arts.
Following her tenure there, her first TV roles included stints on period sitcoms Room 222, Nanny and the Professor and Love, American Style. Later in her career, she would notch up guest appearances in Law and Order: SVU, 7th Heaven and 8 Simple Rules.
Williams also lit up the stage, with theater credits including Death Trap, Nunsense, Grease, Menopause the Musical, Middletown, The Female OddCouple, and a Broadway turn on The Drowsy Chaperone.
She also spearheaded a one-woman show, Me, Myself and Shirley; and wrote a book: Shirley I Jest: A Storied Life.
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On the actress's website, which detailed her current projects as well as houses archival footage and photos, a simple note was added to mark her birth and death years.
"Cindy lit up our lives with laughter," it states.