Liverpool City Council ended its appeal against a government ruling in favour of the area's "Beatles heritage".
A council spokesman said the veto was "illogical" but wanted to avoid "protracted" legal action.
Plans for the site in Dingle, which include Ringo Starr's birthplace, would also have seen 154 new homes built.
The Welsh Streets' demolition was part of a Â£15m regeneration project with social landlord Plus Dane which would have built the new properties.
The Beatles' drummer's former home at 9 Madryn Street was due to be refurbished, along with 36 other properties, leaving 271 other terraced houses demolished.
Nina Edge, secretary of The Welsh Streets Home Group, welcomed the decision adding: "Fingers crossed that Liverpool City Council and Plus Dane have now got an alternative vision for the area."
The city council said: "We still regard the Secretary of State's decision as unreasonable and illogical. However, our priority, rather than engage in protracted legal arguments, is to regenerate the Welsh Streets area."
A spokesman said the council would continue to consult with residents but future demolitions could not be ruled out.
So what now for Liverpool's Welsh Streets in Dingle - once home to one of the Fab Four and subject to years of controversy? One thing is certain, the council doesn't have the money to continue fighting this decision. It says residents will be consulted on how best to achieve "a sustainable and deliverable housing scheme".  Save Britain's Heritage, which owns a house in one of the streets wants more of the houses to be renovated, instead of demolition. Now almost 10 years since residents were moved out that is now likely to happen.
The Â£15m Welsh Streets project had been approved by the council's planning committee and upheld by a public inquiry
But ex-Communities Secretary Eric Pickles rejected the planning inspector's decision saying the proposals were "short sighted as regards the future tourism potential of Madryn Street".
Other reasons included:
Sources differ on how long Starr lived at Madryn Street before his family moved to nearby Admiral Grove, where he was living as a teenager shortly before The Beatles found fame.
The regeneration of Liverpool's Welsh Streets is to continue after the council dropped a legal challenge over the demolition of nearly 300 homes.