The building was known as the Jewish Community Center but has been owned by Bapst High for more than 20 years.
Head of School Mel McKay said it is past time for a new gymnasium for the students who attend the 91-year-old school on Broadway.
He said the gym the school's teams have used for years is much smaller than the regulation 84-foot-long basketball court.
"In this historic building, a basketball court that's 68-feet-long, that has pillars for sidelines. And as you can imagine, students [and] coaches are eager to move into a [larger] space. It's a practice gym space. We'll still call the Cross Center home," McKay said.
McKay said the current gymnasium will be transformed into a dining hall, community center and kitchen.
He said construction is expected to begin within the next few months.