The 83-year-old synagogue would be relocated temporarily during construction before being moved into the new building.
The tower also would include three floors of retail and a hotel with about 260 rooms.
Soho Properties and partner Murray Hill Properties plan to knock down the three-story building, which includes the Garment Center Synagogue on the ground floor, and erect a 23-story tower.
They hope capitalize on the surging hustle and bustle of Times Square, whose central location and popularity with tourists has made it an attractive neighborhood for new hotels.
Last week, the developers and the synagogue reached a deal in which the synagogue agreed to vacate its 49-year home in the coming months so that demolition could begin. The developers made a donation to the synagogue for an undisclosed amount and agreed to relocate the synagogue to temporary quarters before moving it into the new building.
The synagogue held the high cards in negotiations, since it had a 99-year lease for $1 a year. The lease specified that the synagogue would have to relocate temporarily if the building had to be demolished.
Mr. El-Gamal became an internationally known figure when he planned to build Park51, a 15-story Islamic center at 45-51 Park Place, two blocks from the World Trade Center site.
The plan faced protests from opponents who said that a mosque so close to Ground Zero was disrespectful, as well as support from former Mayor Michael Bloomberg and others who said the developers had the right to build a worship space and cultural center.
The developers plan to close on the West 40th Street building in early March.
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