Actor Rock Hudson lost his yearlong struggle against AIDS Wednesday, dying of complications arising from the incurable disease he had helped bring to worldwide attention.

Hudson, 59, a longtime Hollywood star who stunned the world three months ago when he revealed that he was suffering from acquired immune deficiency syndrome, died quietly in his sleep at his Beverly Hills home.

His publicist, Dale Olson, said only members of Hudson's personal staff were present.

Hudson had no close family and memorial arrangements were pending. A spokesman for Pierce-Hamrock Mortuary said the actor's remains were cremated soon after his death.

Learned of Disease in '84

Friends said Hudson had discovered that he had the disease in mid-1984, but chose to continue his acting career while secretly undergoing treatment. He appeared in 10 episodes of television's prime-time soap opera "Dynasty" last season, and was to have continued in the role.

By midsummer of this year, however, ravages of the ailment were plainly apparent. He flew to Paris, where he entered the American Hospital seeking experimental therapy, but stayed just one week before chartering a 747 to return home for treatment at UCLA Medical Center.

It was at this time that he decided to reveal that he was suffering from AIDS--a little-understood and always-fatal ailment that strikes primarily at male homosexuals, intravenous drug users and hemophiliacs.

The reaction from Hudson's friends--and fans--was immediate and heartwarming.

Cards and letters expressing good wishes, sympathy and admiration arrived by the bagful and were still coming in at the time of his death, while his movie colleagues rallied for a star-studded benefit that raised more than $1 million in his name for AIDS research, including $250,000 from Hudson himself.

Help to Others

"I am not happy that I am sick," Hudson said in a message read at the gathering last month. "I am not happy that I have AIDS, but if that is helping others, I can, at least, know that my own misfortune has had some positive worth."

The news of his death brought immediate expressions of grief--one of the earliest coming from President Reagan, who had cheered his former colleague with a telephone call during his stay at UCLA.

"Nancy and I are saddened by the news of Rock Hudson's death," the President said in a statement issued at the White House. "He will always be remembered for his dynamic impact on the film industry, and fans all over the world will certainly mourn his loss. He will be remembered for his humanity, his sympathetic spirit and well-deserved reputation for kindness. May God rest his soul."

Elizabeth Taylor, who is national chairwoman of the AIDS foundation named for Hudson, said, "I love him and he is tragically gone. Please, God, he has not died in vain."

Doris Day Remembers

Doris Day, his former co-star in light comedies such as "Pillow Talk" and "Lover, Come Back," burst into tears.

"Oh, my God, what can I say?" she sobbed. "This is when our faith is really tested. . . . All those years of working with him I saw him as big, healthy and indestructible. . . . Life is eternal. I hope we will meet again."

Bruce Decker, chairman of the California AIDS Advisory Committee, also praised Hudson.