In the period from October to December, gross domestic product expanded by 0.7 percent, bringing full-year growth to 1.6 percent, the federal statistics office Destatis said in a statement.
"The German economy regained momentum at the end of last year," Destatis said.
"After the robust start in the first quarter and subsequent weakness in the second and third quarters, the economy stabilised again in the final quarter."
In a preliminary estimate last month, Destatis had calculated that gross domestic product (GDP) expanded by 1.5 percent in the whole of 2014 and that fourth-quarter growth was "around a quarter of a percentage point."
The main growth driver was consumer spending, the statisticians explained.
Investment was also positive, particularly in equipment and construction.
And both imports and exports also rose strongly, Destatis added.
"The German economy ended a volatile year on a very strong note," said ING DiBa economist Carsten Brzeski.
A more detailed breakdown of the GDP data will be published only at the end of the month.
"But available monthly indicators and the statistical office's statement suggest that domestic demand was the main growth driver. A clear sign that lower oil prices have found their way into consumers' pockets," Brzeski said.
"Looking ahead, the German economy looks set to continue surfing on a wave of economic well-being. With the strong labour market, wage increases, low energy prices and extremely low interest rates, consumers should continue to spend," he said.
Simon Juncker at the DIW think tank in Berlin cautioned that the euro area recovery "remains fragile, not least because political uncertainty has substantially increased again, as Greece has shown."
A new escalation of the conflict between Russia and Ukraine could also dampen companies' investment plans, Juncker warned.
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BayernLB economist Johannes Mayr suggested that the unusually mild weather may have distorted the quarterly growth figures.
"Nevertheless, the outlook for Germany remains positive," Mayr said. "We expect the economy to grow a bit faster in the whole of 2015 than it did in 2014."
Berenberg Bank economist Christian Schulz was also positive.
"The tailwinds from cheap oil, a weaker euro exchange rate and increasingly aggressive European Central Bank monetary policy easing should more than offset the serious short-term risks such as Greece and Russia," he said.
"While the first half of 2015 could still be a little more subdued due to these risks, we expect German growth to reach trend levels a bit above 2.0 percent in the summer 2015," Schulz concluded.