At least three more buses carrying migrants from Texas to New York City are on the way — with one expected to arrive within hours, a City Hall official said Tuesday.

“We’ve learned buses are arriving tonight and two more tomorrow,” Immigrant Affairs Commissioner Manuel Castro told the City Council’s Committee on General Welfare.

Castro also testified that buses chartered by Texas Gov. Greg Abbott to relocate migrants out of the Lone Star State would continue showing up in the Big Apple “basically daily.”

Abbott hired a charter bus company to transport the migrants but the company signed a non-disclosure agreement that prevents the city from getting precise details on its itineraries, Castro told reporters afterward.

“Officially, Gov. Abbott announced that a bus directly from Texas was arriving this past Friday,” Castro testified.

Abbott didn’t “warn us about this even though the bus had started their journey Wednesday and was to arrive Friday,” he added.

Fifty-four migrants got off that bus and another 14 got off a bus that arrived Sunday, with some getting off at other stops, Castro said.

It’s unclear how many more migrants will be on the buses now headed to the Big Apple and how many were expected to disembark here.

Abbott’s office didn’t immediately return a request for comment.

Abbott and Mayor Eric Adams have been trading barbs in an escalating war of words since Adams revealed last month that New York City’s shelter system was being overloaded by asylum-seeking migrants.

Abbott initially denied Adams’ accusation that the Republican governor was sending migrants to New York City but on Friday took responsibility for the bus that caught officials unawares when it showed up at the Port Authority Bus Terminal in Midtown Manhattan.

Abbott — who in April began relocating migrants to Washington, DC, in response to President Biden’s “open borders policies” — called the Big Apple an “ideal destination” because of its generous treatment of homeless people.

City Hall has estimated that around 4,000 migrants have arrived in recent weeks.

Some have told The Post that federal immigration officials directed them here even though they don’t have family or other ties to the city.

Castro testified that “asylum seekers are arriving in a variety of ways,” with many “taking commercial public buses and arriving at many drop-off locations, not just Port Authority.”

Castro said some buses arrive “late in the evening or at night” after stopping first in the nation’s capital “and coming here.”

On Monday, The Post exclusively revealed that the city wants to open a new facility in Midtown Manhattan to process migrants and house at least 600 migrant families, with proposals from non-profit shelter operators due Wednesday ahead of a planned Aug. 15 opening.

Meanwhile, City Hall said Tuesday that 11 emergency shelters had been set up recently, with four in Manhattan, three in Queens and two each in Brooklyn and The Bronx.