There were 81.80 million people living in Germany, the most populous country in the European Union, Destatis said, a gain of more than 50,000 people against the previous year.
With one of the lowest birth rates in Europe, Germany's population has been on a steady decline for most of the past decade.
Last year's rise was due solely to immigration, with deaths still far outweighing births in the rapidly ageing society.
There were between 660,000 to 680,000 births year and between 835,000 and 850,000 deaths, Destatis said, adding that there were at least 240,000 more people immigrating to Germany than those leaving.
"The majority of people in this positive immigration trend came from countries which joined the European Union in 2004, especially Poland," a statement said.
After the labour market of Europe's top economy was fully opened up to other EU members in 2011, an average of 28,000 people per month have flocked to Germany.
Unemployment is at record lows in Germany. Like other advanced economies, Germany is facing a snowballing population crisis, leaving the country short of workers and adding to the strain on already stretched public coffers.
Chancellor Angela Merkel has introduced a raft of measures aimed at boosting the birth rate, including generous parental leave allowances and increasing the number of kindergarten places.