The three acts will be inducted into the Rock & Roll Hall of Fame on May 2, 2020. It was the first time that either of them were nominated.
The artists will officially be inducted on May 2 at the Public Auditorium in Cleveland, Ohio.
Artists who were nominated but not inducted this year are Pat Benatar, Judas Priest, Kraftwerk, Dave Matthews Band, MC5, Motorhead, Rufus featuring Chaka Khan, Todd Rundgren, Soundgarden and Thin Lizzy.
Inductees Houston, B.I.G., late Doobies drummers Michael Hossack and Keith Knudsen, and every T. Rex bandmate save for drummer Bill Legend will be honored posthumously. Meanwhile, Depeche Mode and Nine Inch Nails got the nod on their third nominations.
"We're honoured to be included and to stand alongside the other incredible acts in the Rock Hall and those joining this year", wrote the British synth-pop group on Twitter. "Thank you!" See the band's post below.
Voters seem to have had diversity at least partially in mind: two of the six nominees are black - the Hall's past inductees are overwhelmingly white - although just one (Houston) is female.
"I'm pretty freaked out. I'm quite in shock", Reznor, the band's sole inductee, told Rolling Stone.
"I don't feel like [we] fit in anywhere..." The Notorious B.I.G., né Christopher Wallace, was shot dead at age 24 in 1997.
The inductees are chosen by an worldwide voting body of more than 1,000 artists, including historians, music industry professionals and previous Rock Hall inductees.
This year's inductees to the Rock and Roll Hall of Fame were revealed Wednesday.
Tickets will go on sale to the public on February 27.
For the first time, the induction ceremony will be carried live on HBO, which previously had aired taped highlights in weeks after the actual event.
All remaining tickets will go live on February 27 at the same time.