"Thank U for all your love and support", Jackson tweeted on Thursday.
Jackson's career has spanned over three decades as part of one of music's most important families.
As with the nominees list, each year's inductees are determined by a voting group of "over 1,000" previous winners, historians and members of the music industry.
Thom Yorke of Radiohead performs in St. Gallen, Switzerland. Radiohead finally got their induction this year after many believe they were snubbed in past years.
The solo induction for Stevie Nicks, seen here performing in September, is her second.
Nicks, who was inducted as a member of Fleetwood Mac in 1988, will become the only woman to enter the Hall of Fame on two occasions. The top five artists the public selects comprised a "fans' ballot" and was tallied along the other ballots.
Def Leppard, an English band inducted on its first nomination, kicked off the 80s metal era with stadium-packing guitar anthems including Pour Some Sugar on Me and Rock of Ages.
Radiohead fans were furious a year ago after the band failed to be inducted, but guitarist Ed O'Brien previous revealed his bemusement concerning all things Rock Hall.
Since 1986, the Hall has added 323 inductees to its rolls; they include 220 performers, 33 "early influencers" (a category largely composed of rock and roll's African-American founding mothers and fathers, such as Lead Belly, Robert Johnson and Sister Rosetta Tharpe) and 34 non-performers (generally music-industry executives, but also songwriters, producers and instrument makers). The band, formed in 1970 in the heyday of glam rock, provided a model for the 1980s New Wave scene.
The heyday of British rockers the Zombies' career was the 1960s, with big sellers She's Not There and Time of the Season.