Home prices increased 5.1% in December year-over-year, drastically improving from December 2011 when they were down 4.3% from the year before, real estate data firm Trulia said.

Asking home prices also rose 3.8% year-over-year in November, the largest annual increase to date.

Trulia (TRLA) reported that asking price gains accelerated throughout 2012. The first quarter saw an increase of 0.8% quarter-over-quarter, while the fourth quarter of the year saw a 2.3% rise from the prior quarter.

"The housing market enters 2013 with a running start," said Jed Kolko, chief economist of Trulia. "Price gains picked up steam in 2012, starting with modest increases early in the year and accelerating in the third and fourth quarter."

Phoenix saw the biggest increase in asking home prices, which rose 26% year-over-year in December. However, Las Vegas and Seattle were the two housing markets with the most dramatic turnarounds. Both metros saw more than a 10% gain last year.

Rent prices rose in 2012 as well, up 5.2% from the previous year. Houston, Oakland and Miami saw the largest jump in rent prices. 

In the cities of Houston, Chicago, Philadelphia and Baltimore, rent increases significantly surpassed price increases. However, prices actually grew much faster than rents in Phoenix, Las Vegas, Riverside-San Bernardino and Sacramento. On a national level, prices rose faster than rents in 17 of the 25 largest markets.

"In 2013, rising prices will encourage more new construction and will encourage some homeowners to sell, which will help alleviate the current inventory shortage," Kolko said.