Leaders of the Theater for a New Audience, one of New York’s premier Shakespearean troupes, reached a milestone on Friday in their decades-long dream for a home as they held a groundbreaking ceremony for a $47.5 million theater. The project represents an unusually large financial commitment by the city to move an arts organization — in this case, a critically acclaimed theater company from Manhattan — into Brooklyn.

Scheduled to open in the spring of 2013, the 27,500-square-foot theater will be the first major house for classical work built in New York since the Vivian Beaumont Theater opened at Lincoln Center in 1965, theater and city officials said. The 299-seat main stage includes floor traps that will allow future Calibans to enter from below in “The Tempest,” and a 35-foot height — about twice that of standard Off Broadway theaters — for gods to fly in from the heavens. With better acoustics, conspiratorial and confessional whispers will be audible.

“We’re making the kind of home that artists from all over the world will want to work in,” said Jeffrey Horowitz, who founded the theater company in 1979 and remains its artistic director.

For all the fanfare around the groundbreaking, which drew classical artists like the actor Mark Rylance (a Tony Award winner for “Jerusalem”) and Julie Taymor, who will direct the theater’s inaugural production, Brooklyn artists and politicians had mixed feelings about a Manhattan theater company arriving with substantial support from the city’s limited cultural budget.