Bon Jovi - who skipped the party but participated in Friday afternoon's unveiling of the 2018 inductees plaque and individual exhibits - and the late Nina Simone and Sister Rosetta Tharpe will also be inducted on Saturday.
Founded in London while punk music was exploding, Dire Straits created a unique sound and had a string of radio hits in the 1970s and 1980s, including "Sultans Of Swing" and "Money For Nothing", a song that captured how MTV re-shaped the music industry.
Jon Bon Jovi said he has been writing his Rock Hall speech for years. They went on to record classic rock anthems including "You Give Love A Bad Name", "Livin' On A Prayer" and "Wanted Dead or Alive".
The presenter who'll induct Dire Straits hasn't been announced yet, and only three of the band's members will be on hand for the event: bassist John Illsley, and keyboardists Alan Clark and Guy Fletcher.
The 33rd annual Rock Hall ceremony kicked off with a tribute to Tom Petty, who died in October at age 66.
The band was one of the last to arrive on the red carpet for the 2018 Rock & Roll Hall of Fame Induction Ceremony in Cleveland.
Sambora left in 2013.
New Jersey rockers Bon Jovi, new wave pioneers the Cars and four first-time nominees, including singer Nina Simone, are in this year's eclectic class.
Desmond Child, who co-wrote some of the band's biggest hits, says he'd "love to see them back together". But neither the comedian nor the band showed up that day, and while Stern quickly made up with Kinison, he wouldn't reconcile with Bon Jovi for a few more years.
English rockers Dire Straits were inducted without its leader Mark Knopfler, or his brother David Knopfler.
A flawless Brittany Howard, of the critically acclaimed rock act Alabama Shakes, gave an extraordinary Tharpe impression onstage, winning over the audience with her rousing live performance in honour of the godmother of rock "n" roll.