The 'Livin' on a Prayer' rockers were the frontrunners to receive the honour with a million fans voting for them in the poll.
Frontman Jon Bon Jovi says ''it's about time'' the rock group - who have been eligible since 2008 - were inducted.
Speaking about the honour, Jovi said: ''Well. I mean ... we're very happy about it. And um, you know. It's great.
''I really want to say it's about time.
''Am I relieved? Yeah.
''Am I pleased? Absolutely. But. It's about time.''
Gospel star Sister Rosetta Tharpe was also recognised with an Award for Early Influence.
The 33rd Annual Rock and Roll Hall of Fame Induction Ceremony, presented by Klipsch Audio, will take place on April 14, 2018 in Cleveland, Ohio.
Radiohead, who only made it to 12th place in the ballot, and failed to make the induction, recently played down the honour and the impact it would have had on the ground as a whole.
Other UK artists who made the shortlist were Depeche Mode, Kate Bush, Eurythmics and Judas Priest.
But Radiohead guitarist Ed O'Brien admitted he and his bandmates - frontman Thom Yorke, lead guitarist Jonny Greenwood, bassist Colin Greenwood and drummer Philip Selway - aren't bothered by the nod because to them it's just another awards ceremony.
He said recently: ''It's in our DNA to be a little ambivalent with award ceremonies.
''As a British band, it's one of those things that it's very lovely to be nominated, but we don't quite culturally understand it. It's a very American thing. Us Brits are very bad at celebrating ourselves.''
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