The measure requires at least one female director on the board of each California-based public corporation by the end of next year.
It also requires companies with five members to include at least two women by the end of July 2021, while companies with six or more board members must include at least three women.
Hundreds of businesses are thought to be affected by the law, which applies to any company "whose principal executive offices" are in California.
However a number of large corporations based in California, including Chevron, Netflix and Alphabet - the parent company of Google and YouTube - already have several female directors.
Companies which fail to meet the quota can be fined $100,000 (£76,600) for a first violation and $300,000 (£229,800) for subsequent violations.
The measure was passed by California's state legislature last month and signed into law by Governor Jerry Brown on Sunday, although he acknowledged the bill may not survive legal challenges.
"I don't minimise the potential flaws that indeed may prove fatal to its ultimate implementation," Mr Brown wrote in a signing statement. "Nevertheless, recent events in Washington, DC - and beyond - make it crystal clear that many are not getting the message."
The Democratic governor sent a copy to the US Senate Judiciary Committee, which last week narrowly voted to recommend Supreme Court nominee Brett Kavanaugh, despite allegations of sexual assault made against him.
It is one of several measures affecting women that Mr Brown signed on Sunday, his last opportunity to approve or veto laws before he leaves office.
The governor also approved legislation requiring smaller employers to provide sexual harassment training and banning secret settlements related to sexual assault and harassment.
The bill has faced opposition by a coalition of business groups led by the California Chamber of Commerce, which argued that the quotas were difficult for companies to implement and violate constitutional prohibitions against discrimination.
In a letter, the organisation said it applauded the bill's intention but cautioned that it priortised gender "over other aspects of diversity".
The bill was put forward by California state senator Hannah-Beth Jackson, who said a quarter of California's publicly traded companies do not have any women on their boards.
"This is one of the last bastions of total male domination," she said. "We know that the public and business are not being well-served by this level of discrimination."
Applauding its signing on Twitter, Ms Jackson said "this is a giant step forward for women, our businesses and our economy”.
The bill may lead other US states to follow suit - Massachusetts and Illinois have already passed measures pushing companies to boost their gender balance.