Eleanor Gehrig, the widow of Lou Gehrig, the great Yankee first baseman of half a century ago, died Tuesday night at Presbyterian Hospital. She was 79 years old, and had been ill since last August.

Since her husband's death in 1941, Mrs. Gehrig had lived quietly in her apartment on the East Side. She occasionally visited her upstairs neighbor, the late Jack Dempsey, and regularly went to Yankee Stadium with Mrs. Babe Ruth to attend old-timers' games or the World Series.

She went to the Stadium for the last time last summer for the annual old- timers' game and was announced to the fans while watching from her wheelchair.

The dramatic and tragic story of her nine-year marriage to Lou Gehrig became a familiar one, chiefly because it was told in books and two films. In the first film, ''Pride of the Yankees,'' she was portrayed by Teresa Wright. In the second, ''A Love Affair,'' she was played by Blythe Danner. They Met in Chicago

It was the story of Eleanor Twitchell, a spirited young woman from a well-to- do Chicago family who met the strait- laced star first baseman for the Yankees in Comiskey Park and married him after a long-distance courtship. Those were the days when Babe Ruth and Gehrig were the home run heroes of championship teams, and the Gehrigs became prominent in New York's sporting and social life.

They lived in New Rochelle and later in Riverdale and traveled widely, including a trip to Japan in 1934 with an all-star baseball team. But their life was focused on Yankee Stadium, where Gehrig teamed with Ruth, Lefty Gomez, Tony Lazzeri, Bill Dickey and later Joe DiMaggio, and built a record as the Iron Man of baseball.

But their life together ended when Gehrig, after playing in a record total of 2,130 games in a row, was forced to retire in 1939 with amyotrophic lateral sclerosis, a neuromuscular disorder that came to be known as ''Lou Gehrig's disease.''

His wife said later that she never told him that he was suffering from a fatal illness. Instead, she cheered him at home with frequent gatherings, parties and impromptu performances by Tallullah Bankhead and other friends from the Broadway stage. He died at home two years later at the age of 37.

In her autobiography, ''My Luke And I,'' Mrs. Gehrig said that she never wanted to play the role of professional widow to a celebrity, even though she and Mrs. Ruth were greeted for years as ''the great ladies'' of the Yankees.

''I had the best of it,'' she said. ''I would not have traded two minutes of my life with that man for 40 years with another.'' Cremation Is Planned

Mrs. Gehrig's lawyer, George Pollack, said yesterday that her body would be cremated, according to her wishes, and her ashes would be placed with her husband's. There are no survivors.

George Steinbrenner, chief owner of the Yankees, said in a statement from the team's training camp in Fort Lauderdale, Fla.: ''She was a great woman, and the Yankees have lost a dear friend.''