Sinn Fein has described the decision as a "hugely significant" step forward towards preventing the destruction of the 1916 heritage site.
Following the councillors' decision, Sinn Féin President Mary Lou McDonald reiterated her calls for government to act urgently to prevent the site from being allowed to fall further into disrepair.
Teachta McDonald said: "The legacy of 1916 and Moore Street belongs to the people of Ireland, not to Hammerson, a British commercial developer intent on tearing it down for profit.
"That Dublin City Council has now given full protection to Numbers 10 and 20/21 Moore Street, and partial protection to other important buildings, is a hugely significant step forward.
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"We need to see action now so that the site does not fall further into disrepair.
"Councillors rightly rejected Hammerson’s claim that it would be 'inappropriate and unlawful' for DCC to protect these structures.
"The unanimous nature of this vote further highlights the unacceptability of An Bórd Pleanála's refusal to grant an oral hearing on the appeals against granting permission to Hammerson for their Moore Street plans.
"That refusal undermined the democratic decision of the Dáil, which also unanimously passed a Sinn Féin Bill last year, that would see Moore Street protected as a cultural quarter for this and future generations.
"Hammerson's plans would pave over our history despite the fact that there is a far better and achievable alternative proposed by the The Moore Street Preservation Trust and the Relatives of the Signatories to the Proclamation.
"Dublin City councillors have reinforced that Dáil vote, so I am calling on Michéal Martin and his government to honour both democratic decisions, to stand up for the interests of the people, to take the necessary actions to protect and conserve the historic integrity of the entire terrace from 10-25 Moore Street, and to support the alternative plan to prevent the destruction of the site."
