The move follows a campaign by descendents of refugees from Nazi Germany who are angry that their applications for citizenship have been rejected despite constitutional guarantees.
Britain's 2016 Brexit referendum triggered a jump in applications from the descendants of people who fled there between 1933 and 1945.
"Germany must live up to its historical responsibilities," said Interior Minister Horst Seehofer in a statement, adding that he wanted to help people whose parents or grandparents had to flee.
"With the legal degrees which come into force tomorrow, we will create a swift ruling that is immediately valid for these people to get German citizenship," he added.
Article 116 (2) of Germany's Basic Law states that former German citizens who between 1933 and 1945 were deprived of their citizenship on political, racial or religious grounds and their descendants can have their citizenship restored.
However, the "Article 116 Exclusions Group" represents more than 100 people, mostly of Jewish descent, who have had applications rejected or been told they are not eligible to apply.
Its members, from Britain, the United States, Canada, Israel and other countries, say this is unjust and have challenged the decisions. One common reason for rejection has been that applicants were born to a German mother and non-German father. Until 1953, German citizenship could only be passed on through the paternal line.
Germany received more than 1,500 applications from Britain under Article 116 in both 2017 and 2018 compared with 43 in 2015, before the Brexit referendum.
The new decrees loosen the conditions needed for citizenship, for example by allowing individuals with a German mother and foreign father to have their citizenship restored, provided they were born before April 1953.
Die Welt newspaper quoted Nick Courtman of the Article 116 Exclusions Group as welcoming the move, saying it was helpful but noting that a serious and real solution of the problem could only be achieved with a change in the law.