Despite previously vowing not to accept the honor -- even if they "gave me a million dollars" she said -- Cher was on top form at the star-studded ceremony at the Rocket Mortgage Fieldhouse in Cleveland on Oct. 19.
The icon joked that it was "easier" to divorce from Sonny Bono and Greg Allman than being chosen for induction.
"This speech is gonna be such a c -- shoot -- I wrote it the other day, and then I rewrote it tonight, and I'm dyslexic." she quipped at the beginning of her acceptance speech.
Cher paid tribute to record executive David Geffen -- whom she briefly dated in the 1970s -- for petitioning for her induction.
"It was easier getting divorced from two men than it was getting into the Rock and Roll Hall of Fame. I want to thank my guardian David Geffen because he wrote a letter and sent it to the directors -- and now, ha ha, here I am!" she continued.
Although at one point she joked that she's "a good singer, not a great singer," Cher acknowledged that her auto-tune heavy 1998 hit "Believe" "changed the sound of music forever."
"[With] 'Believe,' I changed the sound of music forever -- and it was an accident. My producer and I were having a fight, with my producer saying, 'Cher, do it better,' " the singer recalled.
"I said, 'Dude, if you want it better, get a different singer.' He called me later and said, 'Cher, I've been playing around with the pitch machine, and I think I've got something,' " Cher continued. "I went back and listened to it, and when it was over, we both jumped up and high-fived each other. And then the head of my record company said 'we can't do that because no one will know it was you.' And I said, 'Yes, that's the deal! That's the great part!' "
Elsewhere, the Moonstruck star shared the advice her late actress and singer mother, Georgia Holt, gave her over the years and noted how important it is for women to "never give up," despite the inequalities they face in a male-dominated industry.
"The one thing I have never done is I never give up. And I am talking to the women, okay -- you guys are on your own. We have been down and out, but we keep striving, and we keep going and we are somebody. We are special, as my mother would say," Cher advised.
Challengers star Zendaya was tasked with introducing Cher.
"Where do I even begin? Cher is not one person. Her name is just as legendary as her legacy. Her voice is so singular that any song she sings becomes a Cher song. She's navigated a multitude of musical genres, defined new ones and reinvented others," Zendaya said.
Zendaya also paid homage to the Hollywood star by donning a golden cutout Bob Mackie gown that was almost identical to the one Cher wore by the designer in 1972.
Lipa kicked off proceedings by performing "Believe" and was joined by Cher herself to finish the iconic tune with the pair twinning in eye-popping black leather ensembles and fishnet tights.