The number of people registered as unemployed in Europe's biggest economy fell by a seasonally-adjusted 27,000 to 2.841 million in December, the Federal Labour Office said.
That is the lowest number since December 1991, although the jobless total came close to these levels in early 2012.
The unemployment rate -- which measures the jobless total against the working population as a whole -- slipped to 6.5 percent in December from 6.6 percent in November in seasonally-adjusted terms, the office calculated.
The jobless rate has never been lower since Germany reunited in 1990 after the fall of the Berlin Wall the previous year.
"The labour market continued to develop favourably, independent of the weak economy," the labour office said.
"The trend in employment remains pointed upwards."
The German economy, Europe's powerhouse, has lost some of its shine in recent months as uncertainty resulting from geopolitical crises such as Ukraine undermined the outlook for recovery.
The new political crisis in Greece is also casting a shadow over the eurozone as a whole, although most commentators believe the fallout from that will remain limited.
Sentiment indicators are tentatively pointing up again. And Germany averted a new recession when gross domestic product (GDP) expanded by a modest 0.1 percent in the third quarter.
Private and government consumption is currently keeping the German economic engine ticking over, while falling investment is preventing a more broad-based recovery, the latest GDP data showed.
GDP "is likely to have expanded only slightly again in the fourth quarter," the labour office said, but added that "slightly stronger growth can be expected during the course of 2015."
Natixis economist Johannes Gareis said the German labour market "has shown great resilience in the course of 2014... and exhibits no signs of spillovers from the current slowdown in economic growth."
In fact, the buoyant labour market "continues to be reliable driver of Germany's growth," boosting household confidence and supporting wage growth and thus private consumption, the expert argued.
Retail sales, for example, climbed for the second month in a row in November, new data showed .
And that was "good news for private consumption growth in the fourth quarter," Gareis said.
Berenberg Bank chief economist Holger Schmieding agreed.
"Germany apparently had an excellent start to the Christmas shopping season. Although the data are volatile and subject to revision, that points to a major gain in German private consumption in the fourth quarter," he said.
"Helped by the massive tailwind from low oil prices, German private consumption will likely be a major pillar of German and eurozone growth in 2015," the economist said.
Nevertheless, Germany must not become complacent, Schmieding warned.
The introduction of a national minimum wage from January 1st "is undermining the very basis of its labour market success," he said.
Postbank economist Thilo Heidrich also felt that the falling trend in unemployment would not be able to maintain its current momentum.
For 2014 as a whole, the jobless total averaged 2.898 million and the jobless rate stood at 6.7 percent, the lowest level since unification.
But that could rise slightly in 2015, even if it would remain very low from an historical point of view, Heidrich predicted.
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