IHS Markit's final services index rose to 52.9 from 51.7 in November. The figure was much higher than the flash reading of 52.0 and far above the 50.0 mark that separates growth from contraction.
The dominant sector also recorded its first increase in new business since August, and business confidence climbed to the highest level since April.
"Despite a final flurry from the service sector in December, it's looking like stagnation at best for economic growth in the final three months of the year," said Phil Smith, principal economist at IHS Markit.
"Nothing spectacular is expected for the opening quarter of 2020, though the signs are that things might be starting to turn, with indicators for new orders and business confidence on an upward trajectory across manufacturing and services alike."
The final manufacturing PMI published last week showed that activity in the sector had contracted for the 12th month in a row in December.
The final composite PMI, which tracks the manufacturing and services sectors that together account for more than two-thirds of the economy, rose to 50.2, signalling a tiny expansion after three successive months of contraction.
(Reporting by Joseph Nasr; Editing by Hugh Lawson)
