The Federal Statistical Office says the population at the end of last year was about 600,000 higher than on December 31, 2015, when it stood at 82.2 million.
The agency says the previous record was 82.5 million, in 2002.
Germany saw net immigration of at least 750,000, while deaths outweighed births by between 150,000 and 190,000.
The agency said in a statement today that the estimates are less certain than in previous years due to changes in the way statistics are processed.