Moorways had been used only by clubs since it closed to the public in early 2016 due to maintenance costs.
Now the city council and clubs have said it is too expensive to continue. It will shut by the end of January.
Double gold medallist Ross Davenport tweeted the awards won by Derby swimmers, while others labelled the move "disgraceful" and "ridiculous".
Moorways, which was built more than 40 years ago, has struggled with maintenance and health and safety issues.
Its loss was made more acute by the ongoing closure of the main pool at nearby Queen's Leisure Centre, due to structural problems, although two other pools remain open for public use at the centre.
Peter Spink, chairman of the City of Derby Swimming Club, said they had met the council several times over rising costs.
"The facility just could not made to be viable in the way it was being operated for any longer," he said.
"So we made the decision that we should pull out sooner rather than later so we could stop incurring further costs."
But former Olympic and Commonwealth swimmer Ross Davenport tweeted: "So glad the city hasn't produced an Olympic Champion, 2 Olympic, 8 World, 10 Commonwealth & 14 European swimming Medals in the past 10 years!"
Paula West was one of a number of people to reply, saying: "Derby Clubs can't even access pool time in their own town, having to travel everywhere else #absolutely disgusted".
The council said it regretted the situation but problems with the Queen's Leisure Centre were "unforeseeable" and it was working towards plans for a new 50m pool on the Moorways site.
However the opening of this has already slipped from 2018 to 2020.

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A former Olympian says he's dismayed one of Derby's last large council-run swimming pools is about to close.
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