After years of trying for more liquor licenses, Boston is on the verge of getting five more - one for the Strand Theatre in Uphams Corner and four for the Bolling Building in Nubian Square.

The State Senate on Thursday gave its final approval to a measure to let the Boston Licensing Board grant the new licenses, following passage in the House of a measure sponsored by state Rep. Chynah Tyler of Roxbury. After one last formal look by the House, the measure would then go to Gov. Baker for his signature.

The licenses would be restricted to use in the two buildings and, unlike most other Boston liquor licenses, could not be sold on the open market, but would instead have to be given back to licensing board to re-issue to new applicants from the specific buildings.

The city owns the Strand, and is hoping to revitalize the 1919 theater, which despite more than $10 million in renovation work under the Menino administration, frequently sits unused. Earlier this year, the Wu administration announced $200,000 in grants to local performing-arts groups for performances there.

One of the first to apply for one of the new Bolling licenses will be Jazz Urbane Cafe, which goes before the Zoning Board of Appeal on Tuesday for zoning approval to open in the old Ferdinand furniture showroom that is now part of the overall Bolling Building.

The bill started as a home-rule petition by the City Council.

City Councilors Ruthzee Louijeune (at large) and Julia Mejia (at large) initially proposed asking for four new licenses for the Bolling Building in March, arguing they would spur further development of Nubian Square and help equalize the number of licenses between Roxbury and wealthier areas along the water, downtown and Back Bay, where restaurant and bar owners are better able to pay the high price of a liquor license in a city where their numbers are restricted by the legislature.

The last time the city has won permission to issue new liquor licenses was in 2014, when then Councilor Ayanna Pressley shepherded legislation that got Boston 75 new licenses, most for neighborhoods outside downtown, the North End, the Back Bay and the waterfront.