"Let's be crystal clear on the scope of this mission", he wrote.
The governor stressed in his statement that the troops will not be used to "round up women and children or detain people escaping violence and seeking a better life".
Brown says he'll deploy about 400 troops.
Governors in the border states of Texas, Arizona and New Mexico have already deployed troops to the border.
Border crossings for the past several years have been heading toward historic lows. The letter was addressed to Homeland Security Secretary Kirstjen Nielsen and Defense Secretary James Mattis and posted on Brown's twitter account with the caption: "California responds". President Trump blasts Oakland Mayor Schaaf, Gov.More news: Hungary inflation edges up to 2.0% in March
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Brown cast his decision as a welcome infusion of federal support to fight transnational criminal gangs and drug and firearms smugglers.
"If he's in disagreement with Donald Trump about the justifications for having the National Guard on the border, then why would he accept it?" he said.
Mattis signed a memo on Friday that authorized the federal government to fund up to 4,000 National Guard troops for the border mission through September.
"The location of Guard personnel - and number specifically working in support of operations along the border, the coast and elsewhere in the state - will be dictated by the needs on the ground", said Brown's press secretary, Evan Westrup. But Brown noted in his letter that the state now has 250 personnel across the state, 55 of whom are stationed at the border, as a part of its program to combat transnational crime.
The governor also noted that the state guard "agreed to similar targeted assistance" under the past two presidents.
State government officials in California said Brown's proposed agreement on the troop deployment had been submitted to the federal government for approval. She added that the administration would work with border state governors in this effort.
In contrast, Texas Republican Gov. Greg Abbott, who is contributing 1,000 troops, embraced Trump's mission the day it was announced, saying it would promote the rule of law and "help ensure we are doing everything we can to stem the flow of illegal immigration".