The figure is slightly below November’s rate of 9.9% but prices were still growing “strongly”, the ONS said.
House price annual inflation was 10.2% in England, 4% in Wales, 5.5% in Scotland and 4.9% in Northern Ireland.
Prices in London showed the highest growth of 13.3% while the South East was up 11.5% and the East 11.4%.
Excluding London and the South East, UK house prices increased by 7.4% in the 12 months to December 2014.
In December 2014, prices paid by first-time buyers were 9.5% higher on average than in December 2013. For existing owners prices increased by 9.8% for the same period.
Charlie Wells, managing director of buying agency Prime Purchase, said: “Despite the slowdown in the housing market towards the end of last year, prices are still rising, driven mainly by London and the South East. As we move into this year, things have got off to an encouraging start with the core market of around £1m to £1.5m very active.
“Those first-time buyers who are getting help from their parents are in a strong position in the market up to £1m and there are also plenty of buy-to-let investors competing in that space.”
Wells said the Stamp Duty changes in December have also resulted in confidence growing from the bottom up with the vast majority of the market benefiting from a reduction in the levy. But he said vendors who were pricing their homes correctly and presenting them well were still selling their homes quickly.
Caution remains among buyers and sellers further up the chain as viewings struggle to convert into sales.
“The general election is giving some homeowners an excuse not to put their property on the market until certainty returns. The reality is that if you have something special to sell then it will always sell, whether a general election is looming or not,” he added.
