The latest MarkitCIPS Purchasing Managers' Index (PMI) survey for the sector gave a reading of 57.8 last month beating forecasts, rising from November's 55.3 low. A reading above 50 indicates growth.
Economists had expected a December reading of 56.1.
The report said UK construction firms ended 2015 with a "robust" level of overall business activity.
It added commercial building increased on the back of improving UK economic conditions, leading to new orders.
Housing activity also showed strong growth, picking up from a 29-month low in November, the report said.
However, the survey cautioned that the overall rate of expansion remained slightly weaker than seen on average over this period.
Tim Moore, senior economist at Markit, said: "UK construction companies finished 2015 in a positive fashion, as overall output growth recovered from November's seven-month low.
"Commercial building was the main engine of growth, with this area of activity expanding at the strongest pace since autumn 2014.
"There was also a rebound in house building activity in December, but momentum was still much softer than the post-crisis highs achieved during 2014."
Moore added that although civil engineering work was marginally down last month, the sector is likely to pick up as new building projects are expected to follow UK winter flooding in the North and Scotland.
Howard Archer, chief UK and European economist at IHS Global Insight, said this was a "reassuring survey", which boosts hopes that the construction sector contributed to UK economic growth in the fourth quarter of 2015.
In the third quarter the construction sector was a drag on gross domestic product growth, contracting 1.9% quarter-on-quarter.
Archer added: "Given the UK's acute housing shortage and its prioritising of more houses to be built, the Government will be particularly pleased to see that house building activity picked up appreciably in December after slowing to a near two-and-a-half year low in November."
On Monday, the CIPSMarkit purchasing managers' index (PMI) said UK manufacturing output ended the year by growing at its slowest pace for three months, due to easing new orders.
The report said factory production in December posted a reading of 51.9, compared to 52.5 in the previous month.
It added that factory output over the whole of 2015 was lower than the previous year.