Boston’s condo market has never been hotter. And now it’s poised to get bigger.

Prices for condominiums in central parts of the city hit record highs in 2015, according to real estate data firm LINK, as wealthy buyers paid up for a limited supply of luxury units.

The median price for condos in nine downtown neighborhoods, South Boston, and Charlestown jumped nearly 10 percent from 2014 levels, to $680,000. Prices for luxury condos — buildings with concierge service and parking — climbed at double that rate, to a median of $1.75 million. That translates into nearly $1,200 per square foot. And four in 10 condos sold above asking price.

“It’s almost as though we’re approaching Manhattan prices,’’ said Debra Taylor Blair, president of LINK. “Demand for urban living is high.’’

Condo prices are climbing faster than the region’s overall housing stock, driven by empty-nesters trading suburban single-family houses for a perch in the city and wealthy international buyers shopping for a home in Boston.

Tight supply is also an issue. While Boston is undergoing an epic building boom, much of the new housing to hit the market so far has been rental apartments, not for-sale condos.

“People want something they can buy now,’’ Blair said. “That’s why you’re seeing this escalation.’’

One of the premier new buildings to come on the market is 22 Liberty on Fan Pier in the Seaport District. Its developer, The Fallon Co., sold 102 units at a median price of $2.76 million, or $1,442 per square foot, according to public records tracked by LINK.

“It did well,’’ developer Joe Fallon said. “What’s special about our product is there’s nothing like it and there won’t be anything like it again.’’

But 22 Liberty is at the front of a wave of luxury residences set to open over the next few years, including another Fallon is building next door at 50 Liberty, Tishman Speyer’s condos on Pier 4, and the 22-story waterfront tower Cronin Development is proposing at 150 Seaport Blvd.

Meanwhile, the Millennium Tower in Downtown Crossing — where one-bedrooms start at $895,000 — is more than 90 percent sold and is set to open later this year. And One Dalton, a 61-story tower that will include a Four Seasons Hotel, launched sales this fall ahead of a 2018 opening.

The high prices at 22 Liberty will probably set the bar for those other buildings, said Sue Hawkes, whose firm, The Collaborative Companies, helps market and sell high-end condos. And those in turn will help set prices for the next generation of condos.

“The pricing of those buildings is going to elevate the pricing of the buildings behind them,’’ she said.

The surge in the condo market is not just a function of ultraluxury buildings at exclusive addresses, though, Hawkes notes. There are new projects under development in the South End, Brighton, East Boston, and Union Square, many targeting 30-something professionals who might be seeking more space or amenities but want to stay in the city. In the Fenway neighborhood, for example, the median price for a condo moderated in 2015, down 2.8 percent, to $461,500, while prices in South Boston increased 12.7 percent, to $548,151.

“We see a lot of people moving up,’’ Hawkes said. “Not multimillion-dollar buyers, but people who bought a condo five or six years ago and now want something more.’’

Developers are gradually shifting to meet that market, planning more condos after a several-year run of building apartments all over town. In the first nine months of 2015, according to city figures, 28 percent of new housing permitted in Boston was for-sale condos, up from 26 percent in 2014 and 17 percent in 2013. In the three months ending Sept. 31, more than 40 percent of permitted units were condos.

Hawkes said she expects that trend will continue as rents — especially at the high end of the market — level out. And if it does, Boston’s condo market will continue to get bigger for several years to come.

Tim Logan can be reached at tim.logan@globe.com. Follow him on Twitter at @bytimlogan.