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."

A judge ordered that access to the popular messaging application be blocked in Brazil for two days from Thursday for its failure to comply with a court order.
Brazilian media reported that the judge wanted WhatsApp to provide investigators with access to the WhatsApp conversation of a suspect in a criminal case.
Brazilians have been expressing their surprise at the suspension and have been joking about how they would spend the next two days without access to the popular messaging service.
A user calling himself simply idiota (idiot) (@euidiotices) made it clear he felt adrift without WhatsApp when he posted the above picture and the sentence: "Me without whatsapp".
He was not the only one to make the connection to the popular film Cast Away.
Karina Ribeiro (@karinaribeiro72) said she would exchange some ideas with Wilson, the volleyball Tom Hanks' character starts speaking to while stranded on the deserted island.
Many others shared what they would do with their newfound time under the hashtag #Nessas48HorasEuVou (#Inthese48hoursIwill), which quickly began to trend.
While many of the users said they would pass the time by watching box sets of popular TV shows such as The Walking Dead and Supergirl, some seemed to have forgotten what a TV was.
Luis Mariz (@LuisMariz) tweeted: "#Inthese48hoursIwill we have a picture at home here that has people talking inside, I'm told it's called TV, does your home have one?"
Others wanted to use the outage to socialise with friends face to face...or even get to know their relatives better, such as user Luanete LS.
Some WhatsApp users clearly feel they have lost touch with their closest ones to a sometimes worrying degree, such as Brenda who said she would use the time to "find out who those strange people in my house are.
Some promised to use the time to read books they have so far struggled to finish or to simply watch the sun rise over Rio de Janeiro.
Many also want to return to the days before mobile communication and spend the next two days visiting people and "hugging them".
A thought shared by Rafaa (@rafa_dalri)...or not when she tweeted: "#Inthese48hoursI will have a social life. Just kidding, there's still Twitter".
The curtain is set to fall on a music venue in Derby where a host of famous acts have thrilled fans for decades.
[NEXT_CONCEPT]
Brazilians angered at the 48-hour suspension by a court of the WhatsApp messaging application have been taking to social media.