Germany has registered 964,574 new asylum-seekers in the first 11 months of the year, putting it on course for more than a million in 2015.
The number of migrants arriving has not slowed despite the winter cold, with a record high of 206,101 in November.
German Chancellor Angela Merkel said in August that the country expected 800,000 asylum-seekers over the year.
Documents leaked in October suggested the government was privately anticipating the arrival of up to 1.5m.
Germany has registered more asylum-seekers than any other nation in Europe, although at about 1% of its population, less per capita than several smaller nations.
Registered asylum seekers are not always accepted however, and rates of success vary from country to country. Fewer than 10% of applicants last year in Hungary - which has one of the highest shares of asylum-seekers in Europe - resulted in a positive decision.
The rate in Germany was 42%, while in Sweden - which registered the highest number of applications per capita - it was 77%. Across the EU, the success rate about 45%.
The number of arrivals in Germany so far this year is four times the total for all of 2014. The figures for November do not contain a breakdown by nationality, but in previous months Syrians, for whom Germany has adopted an open-door policy, have been the largest group at around a third.
The country looks set to receive less than a top estimate of 1.5m reported in October by German newspaper Bild, citing leaked government documents. A spokesman for the government denied any knowledge of the document.
Germany's interior ministry said on Monday the time taken to process applications had been brought down from an average of around seven months in 2014 to five months this year - in part by speeding applications from Syria and from what it defines as "safe countries of origin" - such as West Balkan states.
Meanwhile, the UN refugee agency (UNHCR) said the number of migrants crossing the Mediterranean to Europe fell by more than a third in November, due to poor weather and a Turkish crackdown on people smugglers.
In November, some 140,000 migrants and refugees made the perilous journey across the Mediterranean to Europe, marking a 36.5% drop from October, when a record 220,535 landed on Europe's shores, the UNHCR said.
It remains unclear how the trend will feed into arrival figures in Germany.
Chancellor Angela Merkel's decision to welcome Syrian refugees has won her plaudits in some quarters but sparked a backlash in others, with some senior ministers openly questioning the approach.