Anyone should be able to change their first name or legal gender by applying at a local registration office, where no reason or medical information needs to be provided.
For children under 14 years old, the application must be submitted by their parents. Minors over 14 can do it themselves, but must have their parents' consent.
The new legislation replaces a law from the 1980s. According to this, Germans who wanted to change their legal gender were required to submit reports from psychological examinations and await a court decision.
Even before the new law came into effect, around 15,000 people have submitted applications to change their gender, reports the newspaper Der Spiegel.
Family Minister Lisa Paus describes Friday as "a very special day for all trans people, intersex people, and non-binary people".
From today on, their right to self-determine their gender will be significantly strengthened, she says.
It will take three months for a gender change to be processed, and no further changes will be allowed for a year.