But they voiced fears that plans to shut the Victorian baths in Caledonian Crescent would be revived next year and vowed to carry on the campaign to secure its future.
The swim centre was one of four facilities, including the Crags sports centre on the South Side, earmarked for possible closure as part of Edinburgh Leisure's cuts to meet a four per cent reduction in funding from the city council.
But now Edinburgh Leisure chief executive Charles Winstanley has announced it will not close in the coming financial year.
In an e-mail to Alex Cole-Hamilton, Liberal Democrat candidate for Edinburgh Central, he said: "Edinburgh Leisure has no plan to close Dalry Swim Centre in 2011/12. Despite the reduction in our council funding for next year it has been possible - through a combination of withdrawal from the Crags centre, price increases, and operational savings - to balance the books."
He added: "I can give no assurances beyond this period, since we have no funding commitments from the council.
"However, the board will only consider withdrawal from a facility after all other options have been exhausted."
Residents in the area had mounted a strong community campaign, including a 4000-signature petition.
Maria Kelly, who chairs Gorgie/Dalry community council, said: "We are absolutely delighted. But no-one is going to give us a guarantee a decision to close it will not be taken before the next financial year. I imagine in six months' time this is going to rear its head again. The campaign is not closed."
Mr Cole-Hamilton said the Edinburgh Leisure decision was "great news".
He said: "It was clear that closing the centre would have made a big impact on the local community, which is why so many people joined the now successful campaign."
Edinburgh Central Labour MSP Sarah Boyack said she hoped the strong local support, along with continued use of the facilities by the community, would help to ensure the long-term future of the centre.
"However, I am concerned by what the council's budget will hold in the coming months."