New Square is named after the Ukrainian town Skvyra, where the Skverer Hasidic group originated. The founders intended to name the settlement New Skvir, but a typist’s error anglicized the name. New Square was established in 1954, when the Zemach David Corporation, representing Skverer Grand Rabbi Yakov Yosef Twersky, purchased a 130-acre (0.53 km²) dairy farm near Spring Valley, New York, in the town of Ramapo. At that time, most Skverer members lived in the Williamsburg section of Brooklyn. New Square’s founders had felt that the Hasidic community in Williamsburg was being “threatened by assimilation”, as The New York Times later described it. Construction began in 1956, and the first four families moved to New Square in December 1956. In 1958, the settlement had 68 houses.

The development of New Square was obstructed by Ramapo’s zoning regulations, which forbade the construction of multi-family houses and the use of basements for shops and stores. Multiple families sharing single-family houses said that they belonged to extended families, and businesses in private homes had to be secret. In 1959, the community asked for a building permit to expand its synagogue, located in the basement of a Cape Cod-style house. The Ramapo town attorney requested condemnation of the entire New Square community, claiming that it threatened sewage lines. In response, the community requested incorporation as a village, but Ramapo town officials refused to allow it. In 1961, a New York state court ruled in favor of New Square, and the village was incorporated in July of that year.

After incorporating, New Square set its own zoning and building codes, legalizing the existing houses, and the liens disappeared. Lots were sold, and new houses were built. The basement businesses could trade openly, and new businesses were founded, including a watch assembly plant and a cap manufacturer. Three knitting mills and a used car lot opened, but most men continued to go to work in New York City. A Kollel was opened in 1963. In 1968, Grand Rabbi Yakov Yosef Twersky died; he was succeeded as Grand Rabbi by his son David Twersky.