Just 5.5 percent of workers were jobless in December, when adjusted for seasonal and calendar effects, the federal employment agency, or BA, said in a statement - the same level as in November and an all-time low since reunification in 1990.
"The labour market developed very well in December, the number of unemployed people increased less than usual for the season and companies' demand for new workers grew strongly from its already high level," BA chief Detlef Scheele said.
In unadjusted terms, less representative of underlying trends but closely followed in public debate, the unemployment rate was steady at 5.3 percent, also the same level as in November.
Looking across the whole of 2017, the unemployment rate stood at 5.7 percent, or just over 2.5 million people - also the lowest level since East and West Germany were reunified in 1990.
The figures are flattered by the fact that many of the more than one million migrants and refugees who have arrived in Germany since 2015 have yet to show up in official jobless data.
On the other side of the jobs equation, more people were employed in 2017 than at any time since reunification at 44.3 million, figures from federal statistics authority Destatis released Tuesday showed.
That was an increase of 1.5 percent over the previous year's figure.
"The labour market benefited from a broad-based upturn in the economy," BA chief Scheele said of the full-year data.
High demand for German goods abroad, strong domestic demand powered by consumers and supportive policies from the European Central Bank have buttressed the recovery in Europe's largest economy.
Surveys of consumer, business and investor confidence point to continued good times ahead - even as Chancellor Angela Merkel struggles to put together a governing coalition in Berlin after tricky September elections.
"Workers and jobseekers have every reason to look optimistically into the new year," commented Joerg Zeuner, chief economist at state investment bank KfW.
"I see no sign at present that spirited growth in the Germany economy will tail off soon."