Stevie Nicks, Def Leppard, Roxy Music and The Zombies round out the list, which singles out inductees for having contributed "over 25 years of musical excellence", the Hall said in its announcement on Thursday morning.
The induction ceremony will take place in March 2019 in Brooklyn, New York.
Jackson was among the most high-profile nominees on this year's list, with many deeming her induction in the Rock & Roll Hall of Fame to be long overdue.
She became eligible for the distinction in 2007 and has previously been nominated in 2016 and 2017.
Nicks, who has enjoyed a successful solo career in addition to her work with Fleetwood Mac, joins the pool of inductees in her own name, 20 years after the group earned the accolade from the Hall.
She is one of several performers to be recognised as solo artists as well as as part of a band. All four Beatles have been inducted individually – and the group itself is, of course, on the roster too.
The Zombies had been nominated three times prior.
Radiohead and The Cure had each been up for a possible induction only once before, and Roxy Music and Def Leppard made the cut after their first nomination.
The inclusion of The Cure, Radiohead, Def Leppard, Roxy Music and The Zombies means five British bands were selected this year.
Inductees were picked by a group of 1,000 experts defined as "artists, historians and members of the music industry" from around the world.
Fans also got a say through an online vote.
This year's nominees also included Devo, John Prine, Kraftwerk, LL Cool J, MC5, Rage Against the Machine, Rufus featuring Chaka Khan, and Todd Rundgren.
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