Chrysler Corp., the nation's third-largest auto maker, agreed yesterday to pay $637 million for Gulfstream Aerospace Corp., a business aircraft and defense contractor based in Savannah, Ga.

The purchase, expected to be completed in August, will mark Chrysler's reentry into the high-profit defense business it abandoned in 1982 in a bid to raise money to stay in auto manufacturing.

The Chrysler-Gulfstream transaction is a friendly merger. It comes two weeks after General Motors Corp., the country's biggest car company, outbid competitors with a $5 billion offer to take over California-based Hughes Aircraft Co.

Chrysler and GM's success in acquiring high-technology defense partners leaves Ford Motor Co., the second-largest of the Big Three auto makers, still searching for a mate to help expand its defense/aerospace operations.

The car companies say that their pursuit of aerospace businesses is a logical diversification effort. Defense and auto manufacturing have complementary technologies. They are synergistic, which means that developments in one business can benefit the other, the Big Three officials say.

But Wall Street isn't so sure. "I think the truth is that they have more money at the time than they know what to do with," said David Healy, an auto industry analyst with New York-based Drexel Burnham Lambert.

"I think that they've forgotten about the late 1970s and the early 1980s in their attempts at diversification. I don't really see any synergies between GM and Hughes or Chrysler and Gulfstream," Healy said, reflecting concerns voiced by other analysts who believe that the car companies are simply on a spending binge.

The auto makers, flush with profits from recent strong car sales, are rolling in excess cash. Chrysler has a $3 billion reserve of cash and marketable securities. Ford has $5 billion, and GM reached into its nearly $9 billion kitty to help pay for Hughes.

The car companies say that they aren't being wanton. Defense is big business. For example, the Reagan administration is asking for $39.3 billion in defense research and development for 1986.

As a result, Chrysler Chairman Lee Iacocca privately and publicly has decried his 1982 decision to sell Chrysler Defense Inc. to General Dynamics for $348.5 million.

"I said to myself, 'I must be crazy. I'm selling the only profitable business I have,' " Iacocca said in recent comments to reporters and editors of The Washington Post.

But he said he had to sell Chrysler Defense at that time in order to get cash to fund development of Chrysler's new automotive products -- which have proved successful enough to put Chrysler back into the defense business.

Gulfstream specializes in manufacturing executive jets, such as the new Gulfstream IV, which is scheduled to come on line in 1986.

Gulfstream and Chrysler officials said that there already are $1.3 billion in orders for the Gulfstream IV.

Gulfstream also has expertise in the development of military surveillance aircraft and other high-technology products related to defense.

Chrysler will acquire 100 percent of Gulfstream's 34 million shares of stock at approximately $19 a share. The acquisition will be financed with $310 million in cash and the issuance of $327 million worth of Chrysler Corp. notes.

Gulfstream had sales of $602 million last year.

Allen E. Paulsen, Gulfstream's chairman and chief executive officer, has agreed to remain in his position for five more years, Chrysler officials said yesterday.