Brown said the deployment will happen pending review and approval of the federal government.
Trump has said that he wants as many as 4,000 guard members to assist Border Patrol agents until a wall is built.
While Texas, Arizona and New Mexico responded enthusiastically, California officials, who have clashed routinely with the Republican federal administration over the past year on issues ranging from environmental regulations to the state's "sanctuary" policies, largely stayed silent.
California's "sanctuary" policies limiting cooperation with US immigration agents have been a target for Trump's ire, and in his most recent weekly address he called the state "a border-free zone where thousands of criminal aliens can roam free".
A spokesman for Brown said the location and assignment of troops would "be dictated by the needs on the ground". He said the state's transnational-crime effort now includes 250 personnel statewide, including 55 at the border.
The federal government must agree to California's terms before the troops would be deployed.
Seen in the context of Trump's insistence on "sealing up our Southern Border", as he wrote on Twitter, Brown's announcement was hardly a vote of confidence. "Overall immigrant apprehensions on the border last year were as low as they've been in almost 50 years, and 85 percent of the apprehensions occurred outside of California". Brown added that "there is no massive wave of migrants pouring into California", saying that overall, immigration apprehensions on the border last year were as low as they've been in almost 50 years. He added those were the same reasons he agreed to similar targeted assistance from President Bush and Obama in past years.