SANTA BARBARA, CALIF., AUG. 22 -- President Reagan today signed the Federal Triangle Development Act, which calls for construction of a $362 million federal complex in the nation's capital.

In a statement released here, the vacationing president noted that the development along Pennsylvania Avenue will allow the government "to vacate a substantial amount of costly leased space in the District of Columbia."

The building, among other things, is to serve as an international cultural and trade center.

The center will complete development of the Federal Triangle area, created 60 years ago. Most of the new building's 2 million square feet of space will be used to house parts of the departments of Justice, State and Treasury.

About 500,000 square feet would be used for a trade center, providing space for foreign missions, international, state and local agencies concerned with trade and government-sponsored programs supporting cultural exchange. Plans also call for exhibition space and a visa, passport and permit center.

A private developer will be selected to design and construct the project, then lease it to the federal government for 30 years, after which the government would assume ownership.

Such an arrangement will save the government $281 million over the 30 years, according to a report on the legislation.

Meanwhile, about 50 friends and relatives were invited to the Reagans' ranch for the belated celebration of First Lady Nancy Reagan's birthday, which is July 6.

Her birth date has been a subject of longstanding dispute. Nancy Reagan has said she was born in 1923, but records of Smith College, which she attended, show the date as 1921.