The 54-year-old had been rushed to hospital straight from a rehearsal for 8 Simple Rules For Dating My Teenage Daughter.
The final series, its title trimmed down to 8 Simple Rules, ended in 2005, having won a cinematography Emmy in 2004.
It was the inspiration for the ABC show 8 Simple Rules, starring the late John Ritter.
A New York Times bestseller, the book has proven popular for parents, teenagers, and former teenagers everywhere.
He hates his job, his wife is lazy, his son is dysfunctional (especially with women), and his daughter is dim-witted and promiscuous.
In this sitcom, Charlie, who takes Mike Flaherty's place in later years, is the Deputy-Mayor of New York City, and his team of half-wits must constantly save the Mayor from embarrassment and the media.
Sagal portrayed his wife, the family's voice of reason, Cuoco his eldest daughter, the stock ditzy blonde.
Ritter, an icon in the world of American television for his star turn on Three's Company, died in 2003 from a misdiagnosed thoracic aortic aneurysm.