The Irish Jewish Museum has received permission to knock down 3 to 7 Walworth Road in Portobello as part of the scheme.
The development will consist of a new two-storey museum building with a cafe and synagogue at 3 and 4 Walworth Road in Dublin 8.
The new building is to include archive storage space, a specialist audiovisual room and a staff area.
There will also be an exhibition space at ground and first-level, as well as a new cafe, museum shop and a public space, including a garden.
However, the plans were far from universally popular in the locality, with more than two dozen objections lodged.
Adjoining residents had complained of being overlooked by the new development.
In a submission, Fine Gael councillor Kieran Binchy said he felt the proposal was "too large and bulky for the site".
While he supported the "continued existence and development of the Irish Jewish Museum within what was historically the Jewish quarter of the city", he believed the current plans were unsuitable.
In a letter, Mr Binchy had stated: "The sheer size and scale of the development is completely unsuitable for a row of terraced houses in a residential conservation area."
The scheme risked overshadowing neighbouring houses and gardens, he added.