The statistics office said the population eclipsed the previous record high of 82.5 million recorded at the end of 2002.
In a preliminary estimate for 2016, the statistics office said the population eclipsed the previous record high of 82.5 million recorded at the end of 2002, though the number of deaths in 2016 exceeded the number of births by between 150,000 and 190,000.
Deaths have exceed births in Germany since 1972, with a total of more than five million fewer births than deaths.
However, countering that trend, more than a million people fleeing war and poverty in the Middle East, Africa and beyond flocked to Germany in 2015 and 2016, drawn by its strong economy, relatively liberal asylum laws and generous system of benefits.
Since the height of the euro zone debt crisis, Germany is also attracting many migrants from other European countries such as Greece and Spain.
The figures used to calculate net migration were based on numbers signing up at registration offices. Asylum seekers are initially housed in reception centres and generally only registered later.
Steady economic growth since 2010 and generous pro-family policies by successive governments in recent years have helped lift the birth rate but it is still below the death rate.
German government support for refugees has climbed in recent years.
For 2016 and 2017 the government set aside 28.7 billion euros (30.64 billion dollars) in funding to accommodate and integrate the more than one million asylum seekers who entered the country, the ministry said.