The Assembly Rooms, which opened in 1977, was badly damaged in a huge blaze that broke out in its roof car park last March.
The city council said rebuilding would be too expensive and the venue would be sold to a private company and could be knocked down and the site redeveloped.
As well as live music, the Assembly Rooms also hosted British Open snooker.
Perhaps its most famous musical moment was in 1983, when Morrissey was hit in the eye with a flower during a Smiths gig and fans invaded the stage at the end.
The venue also hosted performances from acts such as The Clash, Paul Weller and Manic Street Preachers and was home to the city's pantomime each year.
City council Labour leader Ranjit Banwait said he hoped the venue would be replaced with "some kind of cultural offer".
The opposition Conservative group said the local authority had dithered over the plans.
Councillor Robin Wood said the venue could have been kept "alive" in the interim until a bidder was found.
He said: "For over a year now we have been wondering what on earth is going to happen. Now we are told the wrecking ball is going to go at it.
"I think it would be much better to refurbish it and reopen it and look at other alternatives. What we will end up with is a pile of rubble and nothing."
Dave Parry, of the Derby Civic Society, said the venue was too big for the market place and never really achieved what it set out to do.
"We would like to see something that would be representative of the city," he said.
"I'm not sure that it is the right place for a cultural thing, but we also don't want to see a supermarket or block of flats there."
The curtain is set to fall on a music venue in Derby where a host of famous acts have thrilled fans for decades.