A total of 685,485 EU citizens arrived in Germany in 2015 while 303,036 left for a net increase of 382,449, the paper reported, saying it had access to data from the Federal Office for Migration and Refugees (BAMF).
Germany's economic success and relatively low unemployment has drawn people from the EU's poorer members in search of work and better lives.
Romanians topped the list of new arrivals in Germany last year with nearly 175,000, followed by Poles with almost 150,000 and Bulgarians with just over 70,000, Die Welt said.
In April, Germany tabled a proposed law to drastically limit EU migrants' access to welfare payments.
Die Welt said a total of 4.1 million EU citizens currently live in Germany.