Prophet, 59, said she will retire "sometime during the summer of 1999," the church announced in a press release.
She told her followers of the decision Friday at the church's annual New Year's conference in Miami.
Her malady was diagnosed as Alzheimer's in November but she had been suffering from what the church called an undiagnosed neurological disorder for a year prior to that.
However, three of her adult children said in an open letter to church members posted on the Internet last week that they believe she has suffered from Alzheimer's for at least five years.
Diagnosis of the disease "helped to explain some of the difficulties we have had in our relationships in the 1990s," Sean, Erin and Moira Prophet wrote in the letter.
Erin Prophet declined to comment for this story but in the past has said the church faces an uncertain future without her mother.
The church was built around Elizabeth and her husband Mark Prophet, who founded the church in the late 1950s and died in 1973.
Prophet had earlier resigned her position as church president but retained her role as spiritual leader, in which she takes "dictations" from an array of Ascended Masters, spiritual entities that church members believe speak only through her mouth.
Church spokesman Christopher Kelley said Saturday he is not aware of a designated successor but said he is confident the church will survive.
The Mormon church also had a turbulent and controversial period in its early years in the 19th century but Kelley noted that the church prospered and grew after the death of its founders.
"It's the teachings, not the personality, that has a real holding factor," Kelley said. "That's the glue of the church membership."
The church teaches an eclectic mix of Eastern and Western philosophies. Its theology combines notions of karma, reincarnation and many aspects of traditional Christianity.
Still, Prophet has been the church's central and driving force since Mark Prophet's death. Her role as a charismatic leader, one whom many have accused of abusing and cheating her followers, has led critics to label the church as a cult, a description church loyalists strongly dispute.
The church moved its headquarters from California to a 12,000-acre ranch at Corwin Springs, adjoining Yellowstone National Park, in 1986. It has been a prominent and often controversial presence ever since, especially during the "shelter period" of 1989-90 when members flocked here to be near bomb shelters in the event of nuclear war or other catastrophe.
Loyal followers refer to Prophet as Mother or Guru Ma and maintain she has showed them the way to spiritual enlightenment. But many former members maintain she is a megalomaniac who has abused church members, overworking them in her personal service and bilking them of money.
One former member successfully sued her and the church for fraud and other offenses and won $1.5 million, a verdict upheld by the United States Supreme Court.
Over the past two years, church leaders have been preparing for Prophet's eventual absence. Some religious scholars have said such preparations are necessary if new religions are to outlast a charismatic founder.
The church has laid off hundreds of employees, sold millions of dollars worth of land and other assets, and re-organized its structure. Its new focus is on outreach around the world instead of on activities at church headquarters.
For years, Prophet and her immediate family ran the church by dictate, both current and former members have said.
Now, two separate boards of directors make decisions formerly made by Prophet or her last husband, Ed Francis, who resigned from the church in 1998, though he still sits on church boards.
Peter Arnone, a former church member living in Livingston, said he doesn't believe the church can survive without Prophet at the helm.
"They won't have that charismatic leader any more to be that cohesive force," Arnone said. The new leadership "is grasping at straws to defend its history, to defend its leadership."
Kelley said church leaders have recently committed to a retirement package for Prophet worth approximately $67,000 a year.
Prophet's retirement compensation became an issue with her announcement that she has Alzheimer's. Sean, Erin and Moira Prophet are seeking legal guardianship of their mother, as is church vice-president Murray Steinman.
Kelley said the church intends to take care of its leader.
"Church members love Elizabeth dearly and want to make sure she's taken care of for the rest of her life," Kelley said.
Prophet has a fourth adult child, Tatiana, who has stayed out of the custody dispute. Her fifth child, Seth, is four years old. She also has eight grandchildren.