By Devika Krishna Kumar

Sept 30 (Reuters) - California will require publicly listed companies with headquarters in the state to have at least one woman on their boards of directors by end of 2019, under a bill signed into law on Sunday.

The law would mandate at least two female directors by the end of 2021 if the company has five directors and three women if the company has six or more directors. Violators face fines of at least $100,000 and up to $300,000 for multiple violations of the statute.

"Given all the special privileges that corporations have enjoyed for so long, it's high time corporate boards include the people who constitute more than half the 'persons' in America," California Governor Jerry Brown said in a statement announcing the bill's signing.

Silicon Valley tech companies started disclosing workforce diversity figures in 2014, but progress at the top has been slow, underscoring the challenge of transforming cultures that critics say are too homogenous, white and male dominated.

Companies including Apple Inc, Google parent Alphabet Inc and Facebook Inc are headquartered in California and will each need to add at least one more woman to their boards by 2021 to meet the law's requirement.

Companies have faced scrutiny in recent years on the composition of board directors and workforce diversity, with investors pushing to get more women onto boards.

"There have been numerous objections to this bill and serious legal concerns have been raised ... nevertheless, recent events in Washington, D.C. - and beyond - make it crystal clear that many are not getting the message," Brown said.

On Friday, President Donald Trump, under pressure from moderates in his own party over Supreme Court nominee Brett Kavanaugh, ordered an FBI investigation into sexual misconduct allegations against Kavanaugh, including by a California professor.

The move came after an extraordinary hearing in which Palo Alto University professor Christine Blasey Ford detailed a 36-year-old sexual assault allegation against Kavanaugh.

The bill signed by Brown highlighted a six-year study conducted by Credit Suisse of more than 2,000 companies worldwide that showed having women on boards was linked to improved business performance for key metrics, including stock performance. (Reporting by Devika Krishna Kumar in New York; Editing by Meredith Mazzilli)