The latest Markit/CIPS purchasing managers' index (PMI) was at 51.4, rising above the 50 mark, which signals expansion, for the first time since March.
It was also the highest reading since September 2011, helped by demand from domestic customers which offset the ongoing dip in orders from the troubled eurozone.
Although it is still likely that manufacturing contracted in the fourth quarter, many economists believe the sector is now stabilising, which may improve the performance of the wider economy.
Howard Archer, from IHS Global Insight, said: "The marked pick-up in manufacturing activity in December is a significant boost to hopes the economy was at least flat in the fourth quarter and could even have grown marginally.
"While the purchasing managers' survey offers real grounds for hope for manufacturers as they head into 2013, it is evident the sector still faces tough domestic and global conditions."
Output increased for the second month in a row, with the rate of growth the strongest in 20 months.
However new export orders dipped again and backlogs of work continued to decline.
Employment fell slightly while firms also signalled they had greater spare capacity.
David Noble, chief executive at the Chartered Institute of Purchasing & Supply, said: "In what has been a difficult year for the manufacturing sector, it is very encouraging to see 2012 end on a high with a second consecutive increase in output and the strongest rate of growth in 20 months presenting a more solid platform for 2013.
"This is largely a reflection of improved performance in the domestic market.
"But the sector is far from out of the woods. The decline in new export orders demonstrates that challenging global economic conditions and the eurozone crisis continue to act as a drag.
"Moreover, the slight fall in employment, increased costs and spare capacity are warning signs for the year ahead."
That cautious view was echoed by Samuel Tombs, from Capital Economics.
He predicted manufacturing would contract by around 0.7% overall in the fourth quarter, and added: "With the recession in the eurozone set to deepen and consumers at home on course to be hit by a further bout of relatively high inflation, 2013 is shaping up to be another tough year for UK manufacturers."