Danny Thomas, the comedian and philanthropist best known as the star of the television series "Make Room for Daddy" in the 1950's and 60's, died yesterday at Cedars-Sinai Medical Center in Los Angeles. He was 79 years old.

He died after a heart attack at his home in Beverly Hills, a hospital spokesman said.

Mr. Thomas appeared in "Make Room for Daddy," later known as "The Danny Thomas Show," from 1953 to 1964, playing a nightclub comedian, which he was for much of his almost 60-year career. He was also a founder and benefactor of the St. Jude Children's Research Hospital in Memphis, which seeks cures for children's cancer and other catastrophic diseases.

"Danny was one of the giants of the industry," Bob Hope said yesterday. "And what he did for St. Jude's will never be forgotten."

Phil Donahue, the television talk-show host who is married to Mr. Thomas's daughter Marlo, said: "He hit the long ball for such a long time. He would hold an audience for an unprecedented length of time in the imagery of the story he was telling, and suddenly would come the punch line, and the ceiling would crack with laughter. He wove an illusion on the stage with no props, all by himself." A Title Taken From Life

Mr. Thomas returned home recently after completing a nationwide tour promoting his autobiography, "Make Room for Danny," written with Bill Davidson and newly published by G. P. Putnam's.

The comedian said in his autobiography that the original title of his television show was provided by his wife, the former Rose Marie Cassaniti. The title was based on their family's many years of experience with his nightclub travels. While he was away, his two daughters slept in his bedroom with their mother and put their clothes in his dresser. When he returned home, they would have to clean out the dresser to "make room for Daddy."

Danny Thomas was born on Jan. 6, 1912, on a horse farm in Deerfield, Mich., the son of Lebanese immigrants. Many references list the year of his birth as 1914, but a family spokesman said yesterday that it was actually 1912. At birth he was named Muzyad Yakhoob, but his parents later changed the name to Amos Jacobs. He grew up with his eight brothers and one sister largely in Toledo, Ohio, and dropped out of high school in his freshman year with a dream that many first-generation Americans had in those days: to make it in show business. He had already, at age 11, had his first job in the entertainment world: selling candy and ice cream in the aisles at a burlesque house. He made his official show-business debut in 1932 on "The Happy Hour Club," an amateur show on WMBC Radio in Detroit.

On Aug. 12, 1940, at the 5100 Club in Chicago, he took the name Danny Thomas, Danny after his younger brother and Thomas after his eldest. He had already acted on radio -- his true ambition was to be a character actor -- but took the club job because the pay, $50 a week, was better than his radio salary. He did not, however, want his radio friends, or his family in Toledo, to find out that he had returned to the saloons, so he came up with a pseudonym. It stuck. A Comedian's Style

It also soon became clear that his forte was comedy. He was spotted by Abe Lastfogel, then the head of the William Morris Agency, who guided his career for many years.

As a comedian, Mr. Thomas was a storyteller, not a specialist in one-liners. "My people are inherently storytellers," he said in a recent interview. "When I was a kid, the entertainment was somebody from the old country or a big city who came and visited and told tales of where they came from. And my mother was very good at it. She could not read or write in any language, yet she would see silent movies and make up her own scenarios."

In the 1940's, Mr. Thomas performed on the Fanny Brice radio show and then was given his own program on CBS radio, "The Danny Thomas Show," which ran from 1944 to 1949. In World War II, he entertained troops in North Africa, Italy and the Philippines, and after the war he went into the movies.

Three movie producers -- Jack Warner, Louis B. Mayer and Harry Cohn -- wanted him to fix his trademark hook nose, saying that otherwise he would never make it big. Mr. Thomas adamantly refused.

His films included "The Unfinished Dance" (1947); "The Big City" (1948); "Call Me Mister" (1951); "I'll See You in My Dreams" (1951), in which he starred, opposite Doris Day, as the songwriter Gus Kahn, and "The Jazz Singer" (1953), in which he portrayed Al Jolson. From Performer to Producer

Then came the television series, which lasted 11 years. It began on ABC and was switched to CBS. The show can still be seen in reruns. The series made him a household name. Mr. Thomas recently recalled that the program was frequently No. 1 in the ratings and almost always in the top 10.

He then became a highly successful television producer, first with Sheldon Leonard and then with Aaron Spelling. The series he produced with Mr. Leonard included "The Andy Griffith Show," "The Dick Van Dyke Show," "Gomer Pyle, U.S.M.C." and "The Real McCoys"; those with Mr. Spelling included "The Mod Squad" and "The Guns of Will Sonnett." Later television series in which Mr. Thomas starred included "Make Room for Granddaddy" in 1970, "The Practice" in 1976 and 1977, "I'm a Big Girl Now" in 1980 and "One Big Family" in 1986.

Throughout his television career, Mr. Thomas continued to perform in nightclubs. In recent years, he appeared in a Legends of Comedy act with Milton Berle and Sid Caesar. In 1985, President Ronald Reagan gave him a Congressional medal for his achievements. Creating a Shrine

Mr. Thomas, a Roman Catholic, was long known for his strong religious faith. He often said that in the difficult early days of his career, when his wife was urging him to give up show business and get a regular job, he prayed to St. Jude Thaddeus, the patron saint of hopeless, impossible and difficult cases. He asked the saint to put him on the right path, vowing that if the saint did so he would build him a shrine.

That shrine, built with the assistance of many other people, was the St. Jude Children's Research Hospital, which was dedicated in 1962. Mr. Thomas spent much of his time raising money for the hospital, which he long considered his most important accomplishment. "That's my epitaph," he said in a recent interview. "It's right on the cornerstone: Danny Thomas, founder."

He was also devoted to his family and loved to talk about the success of his children: Marlo Thomas's career on television and in films, his daughter Theresa's two children, the work of his son, Tony, as a producer of television shows and films, including "The Golden Girls," "Empty Nest" and "Dead Poets Society." On Saturday night, Danny Thomas appeared as a guest on "Empty Nest," portraying an elderly physician.

In addition to Mr. Thomas's wife and three children, survivors include five grandchildren.