The band, which has been effectively retired since the mid-'90s, joins Bon Jovi, The Cars, The Moody Blues, Nina Simone and Sister Rosetta Tharpe as the institution's 2018 inductees.
Known for hits like "Money for Nothing," "Sultans of Swing," "So Far Away," "Romeo and Juliet" and many others, Dire Straits appeared on the ballot this year for the first time and finished third in fan voting behind Bon Jovi and the Moodys.
Illsely told Billboard that he's honored at the recognition.
"I still consider [Dire Straits] to always be a rock n' roll band; first and foremost that's where we came from," he said. "So to be part of the Rock and Roll Hall of Fame is like ticking off a pretty large box."
Dire Straits frontman Mark Knopfler, who has showed little interest in reuniting the band since it's break, hadn't commented publicly on the honor as of Wednesday evening ET, except to share the news via his Facebook fan page.
Illsley tells Billboard he's not sure whether Knopfler would be interested in performing with his former band at the induction ceremony.
"Mark is quite sort of restrained about things like this," Illsley notes. "We have spoken about [the induction], and we just said, 'Oh, that's nice.' I think it would probably be important if Mark and I were there. I'll definitely be there, and I'll definitely talk Mark into coming as well. It's essentially up to him if he wants to do anything, and I completely respect his feelings about it. He doesn't want too much white light."
Illsley and Knopfler are the only two original members of Dire Straits to see the band through to the end.
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Photo: Instagram / JohnIllsleyMusic