The law, which Germany's lower house of parliament passed on Friday, will make it compulsory for the supervisory boards - in other words non-executive boards - of 108 German companies listed on the stock market to be made up of at least 30 percent women as of January 2016.
Family Minister Manuela Schwesig said it was "an historic step" for Germany and "an historic day" for equality. German Justice Minister Heiko Maas said the bill was "the biggest contribution to equality since women were granted the right to vote."
The bill has been criticized for not going far enough as it only applies to supervisory boards. The Greens, the Left party and some Social Democrats are in favor of introducing much higher quotas for women in leading positions.
The conservative Christian Social Union (CSU) and some Christian Democrats had pushed for the bill to be delayed to soften the impact on the economy, which was weaker when the bill was first mooted.
Business federations are also skeptical because of the bureaucracy involved.
The quota was negotiated near the end of 2013, but a formal accord among Germany's three-party grand coalition was not reached until a year later. Chancellor Angela Merkel's cabinet approved the plan in December.
Small businesses will also be required to take steps to improve workplace equality, with the quota being introduced on a sliding scale in terms of the size of the company. Around 3,500 companies would be affected.
From 2017, smaller companies and public services must report on their progress in increasing the number of women in leadership positions, but they will not be penalized if they do not meet the quota.
The bill still has to be approved by Germany's upper house, the Bundesrat.
ng/kms (dpa, Reuters )