Millennium Tower, the 685-foot, 442-unit skyscraper being built by Millennium Partners at Downtown Crossing, opens its sales office to the public Thursday morning. But a third of the units already have purchase and sales agreements in place, developers claim.

"Our timing is good. And there really isn’t anything like this on the market, not just here in Boston, but anywhere in the country, I’d even say the world," said Richard Baumert, partner at Millennium Partners. Residents of Millennium’s existing properties were able to obtain previews of the building for the past several weeks, Baumert explained, and about 150 of the units already have signed purchase and sale agreements in place.

The tower is due to open in the summer of 2016. It will feature a two-story club and lounge; a fitness area, which includes a lap pool and steam rooms; a bar;a full-service kitchen whose menu will be managed by Michelin-starred chef Michael Mina; a 24-hour concierge and full-time staff dedicated to arranging social and educational events for residents.

The building will be topped by a five stories of penthouse units, starting at $7 million. Three are already under agreement, said Baumert, though not the very top floor, a floor-through unit being offered, as an unfinished shell, for $37 million.