© Carlo Allegri / Reuters
The lawsuit claims the California bill is "unlawful and anti-consumer" because it goes against the federal government's policy and regulates the Internet.
The bill signed by Brown (D) is the country's strictest net neutrality bill.
The new California legislation bars internet service providers from slowing down website speeds, blocking access to certain websites and charging extra for large websites such as Netflix and Facebook.
State legislators began crafting the legislation last year when the Trump administration rolled back net neutrality rules.
California Attorney General Xavier Becerra in a statement after the bill's signing said it was a win in the battle against the president's agenda.
"While the Trump Administration continues to ignore the millions of Americans who voiced strong support for net neutrality rules, California - home to countless start-ups, tech giants and nearly 40 million consumers - will not allow a handful of power brokers to dictate sources for information or the speed at which websites load," Becerra said.
U.S. Attorney General Jeff Sessions said the federal government should have ultimate authority over net neutrality policies, the AP reported.
Telecom companies have rallied against the bill since it was first introduced. The United States Telecom Association in a statement said it agrees net neutrality should be the purview of the federal government.
The battle over net neutrality has been fraught since the Federal Communications Commission last year rolled back Obama-era regulations that said all traffic on the internet should be treated equally.
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