Southern California’s housing market ended last year with sharp home-price gains and the highest sales for a December in three years.

The region’s median home price rose 19.6% in December over the same  month last year to hit $323,000, real estate firm DataQuick reported. A record level of cash buyers flooded into the market and more move-up homes also sold last month.

“The housing market had more to offer in 2012 than many anticipated,” DataQuick President John Walsh said in a statement. “A lot of markets not only found a price bottom as foreclosures waned, but they started to see their first meaningful gains in nearly two years.”

The rise in the median, which is the point at which half the homes in the region sold for more and half for less, was essentially flat from the prior month, up only 0.6%. San Bernardino and Riverside counties posted the strongest year-over-year increases, up 20.0% and 19.1%,  respectively, indicating that the once hard-hit Inland Empire is now probably in recovery.

An estimated total of 20,274 new and previously owned homes and condominiums sold throughout the six-county region. That was a 5.1% increase from November and up 5.3% from December 2011. Last month’s tally was the highest for a December since 2009.

Last year was the first year of solid improvement since housing crashed in 2007. The strong performance last month indicates that 2013 will also continue to bring home price gains, analysts said.

The gains came as foreclosures declined, housing inventory plummeted, mortgage interest rates hit record lows and demand from investors spiked. The overhang of the last housing bust also resulted in some unexpected benefits.

For instance, the high number of underwater borrowers — or those homeowners who owe more on their mortgages than their homes are worth — actually served as a boost to the market rather than being a drag, as people kept their homes off the market, decreasing inventory.

“The lock-out phenomenon, combined with the rise in investors converting foreclosures intro rentals, lead to a lack of for-sale inventory,” CoreLogic economist Sam Khater wrote. “With home prices rising in 2012 and 2013, tight for-sale inventory will begin to ease.”

Nationally, CoreLogic reported that home prices were on a sharp upward trajectory in November, with almost all states posting gains that month. The firm’s home price index report, also released Tuesday, showed that home prices nationwide increased 7.4% year-over-year.

“Consistent price increases throughout 2012 have started the process of lifting households out of negative equity, which will support home sales and refinancing volumes,” Paul Diggle, an economist for Capital Economics, wrote in an emailed analysis. “Lower levels of negative equity is good news for housing market activity and sets up a virtuous circle of rising activity leading to rising prices and pushing negative equity down further.”

In California, buyers can anticipate little new inventory on the market. A supply of only about 2 1/2 months’ worth of single-family homes for sale was available statewide at the end of December, the California Assn. of Realtors reported Tuesday. A supply of six or seven months is considered healthy by most economists.

Supply from distressed sales, particularly from foreclosed homes, will remain tight as those homes are being quickly snapped up by investors even as the number of troubled borrowers entering foreclosure continues to decline. The number of notices of default — the first step in the formal foreclosure process — fell 14.5% in December from November and dropped 39.8% from December 2011, according to foreclosure tracker ForeclosureRadar.com. The decline in foreclosures has been aided by an increase in short sales, as The Times recently reported, as well as other loan modifications for borrowers. The drop in foreclosures should continue to help lift prices.

“For 2013, we largely expect more of the same,” Sean O’Toole, chief executive of ForeclosureRadar, wrote in a blog post this week. “Demand will remain strong thanks to Federal Reserve-manipulated low interest rates and affordability. Housing supply will remain constrained, largely due to government foreclosure intervention. As a result, prices will rise, though likely at a slower pace.”

The increase in the median home price is also being heavily influenced by the change in Southern California’s market dynamics as fewer sales are logged in cheaper neighborhoods and pricier places take off. Throughout Southern California, sales of mid-to-higher-cost markets rose in December, DataQuick reported. Sales of homes between $300,000 and $800,000, the typical move-up range, jumped 31.4% year-over-year. Sales of homes above $500,000 soared 40.0% year-over-year, while sales of homes of more than $800,000 were up 36.3%.

Meanwhile, cheaper neighborhoods posted weak sales. Most notably, the number of homes throughout the region that sold below $200,000 dropped 28.1% while those below $300,000 fell 18.2%.

Sales of foreclosed homes made up just 14.8% of the market last month, down from 15.4% the month before and 32.4% in December 2011. That compares with a high of 56.7% of the market in February 2009. Cash buyers and investors are also playing a big part in snapping up home inventory. Cash buyers bought up 33.8% of all resale homes last month, while absentee buyers purchased 29.1% of Southland homes in December, DataQuick said.

Join us for a live video chat at 1:30 p.m. with DataQuick analyst Andrew LePage, Zillow.com chief economist Stan Humphries and USC’s Richard Green, director of the Lusk Center for Real Estate.