"Cher is very supportive and has known about Chastity wanting to do this for a very long time," a source tells PEOPLE. "This will be a long process but it's something Chastity has wanted to do for many years."
Bono's spokesman, Howard Bragman, told , which first reported the story, "Yes, it's true – Chaz, after many years of consideration, has made the courageous decision to honor his true identity.
"He is proud of his decision and grateful for the support and respect that has already been shown by his loved ones. It is Chaz's hope that his choice to transition will open the hearts and minds of the public regarding this issue, just as his 'coming out' did nearly 20 years ago."
He added, "We ask that the media respect Chaz's privacy during this long process as he will not be doing any interviews at this time."
Cher 'Flipped Out'According to a about Bono, at the time she published her book, Family Outing, a guidebook of real-life examples (including her own) that showed young gay people the rewards and pitfalls that accompany being open about their sexuality, Bono first decided to tell her parents she was gay when she was a freshman at New York University in fall 1987. Father Sonny took the news in stride, but mother Cher did not.
"I flipped out," Cher told PEOPLE. "I'd always had this idea that she would get married and have a family." And though Cher had won acclaim for her portrayal of a gay woman in the 1983 film Silkwood – and has counted upon gay audiences for being among her staunchest fans – she banished her daughter from her Manhattan apartment. Later, when Chastity decided to abandon her studies to pursue a career as a rock singer, she chose to keep her homosexuality a secret.
It didn't work. While she was trying to launch a career with her band Ceremony in 1990, a weekly tabloid announced Bono's lesbianism to the world. Besieged by reporters, she also felt betrayed by members of the gay community, who had tipped off the tabloid.
"It was the most traumatic thing that ever happened to me," she said in 1998. Bono felt completely at sea. "I closed my blinds at home," she said. "I didn't have a life, really."
Parents AcceptedIn 1992 she began a serious relationship with "Joan," a woman 20 years her senior, which ended tragically when the woman lost a battle with lymphoma and died in 1994. Finally, in 1995, Bono publicly embraced gay activism by posing for the cover of the gay magazine The Advocate, proclaiming herself "out at last" and taking a high-profile job with the Gay and Lesbian Alliance Against Defamation (GLAAD).
Bono's activism transformed her relationship with both parents, sparking pride in her mother, who "got to see me as a full person for the first time," said her daughter. But Sonny was by then a Republican congressman whose conservative agenda did not include gay causes such as legalizing same-sex marriage. "He accepted me, but his politics didn't," Chastity recalled. (Sonny Bono died in January 1998.) "I didn't talk to him about it, but I was angry."