WASHINGTON (AP) _ President Reagan has written Philippine President Corazon Aquino, congratulating her on the overwhelming vote of approval for the nation's new constitution, White House spokesman Marlin Fitzwater said today.

The spokesman issued a statement lauding the plebiscite as a ''significant milestone on the path to democratic renewal which President Aquino has charted for the Philippines.''

''We congratulate the people of the Philippines on their latest successful exercise in democracy and wish them equally well in the political contests ahead,'' Fitzwater said.

Saying that the United States ''encourages vigorously and supports totally'' the institution of civilian government in the Philippines, the spokesman said the U.S. government pledges ''continuing support for President Aquino's courageous efforts to maintain her fellow Filipinos' freedom and participation in the political process.''