The adjusted jobless rate fell to 6.8% from 6.9% in November, the Federal Labour Office said.
This marked a new record low since figures for unified Germany were first published.
The seasonally-adjusted total for the number of people out of work in Germany fell 22,000 to 2.88 million in December.
The agency said the number of people out of work averaged 2.976 million over the course of last year.
News of the figures saw the German Dax stock exchange rise almost 1% by noon on Tuesday.
This was equal to an average jobless rate of 7.1 % - down from 7.7% in 2010.
Leading economists expect Germany's economic growth to slow in 2012, however, in line with other major eurozone economies, which may put a squeeze on wages and jobs.
But, as the BBC's Berlin correspondent Stephen Evans points out, unemployment at a record low for the last two decades is something most countries would envy, and a sign of the way Germany has rebuilt itself since the Wall came down.Strong exports
"Germany's manufacturing and export-driven economy finished the year strongly - piling on another 22,000 jobs in December," said Anthony Cheung of market analysts RANsquawk.
"Behind the strong performance lie some adept moves by Germany's exporters.
"As their eurozone markets weakened, they have been very good at moving their focus elsewhere.
"German carmakers have more than compensated by dramatically growing sales to developing markets."
By contrast, Spain said on Tuesday the number of people claiming unemployment benefits stood at a 15-year high at the end of 2011.
The Spanish claimant count is now 4.42 million, with December seeing the fifth straight monthly rise.
BBC
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