GREENWICH, Conn. (AP) _ Primerica Corp., the former American Can Co., said Wednesday it agreed to acquire the closely held investment firm Smith Barney Inc. for $750 million in cash.

Smith Barney is the New York-based parent of Smith Barney, Harris Upham & Co., a medium-sized investment bank and securities brokerage that is one of Wall Street's oldest firms, founded in 1873.

The 86-year-old Primerica Corp. completed its five-year transformation from a manufacturing company to a financial services and specialty retailing firm in March. Primerica has interests in insurance, mutual fund and mortgage banking services.

The Greenwich-based company, which sold its container operations last year, adopted its new name on April 28 to reflect that change.

Smith Barney apparently became available for sale earlier this month when a group of wealthy Arab investors, who collectively owned 22 percent of the firm, put their stake up for sale. The rest of Smith Barney is owned by its current and former employees.

Primerica said the proposed merger was subject to approval by Smith Barney's stockholders. But the 33 Arab investors and holders of an additional 11 percent of Smith Barney's shares already had agreed to vote for the transaction, the company said.

After the announcement, Primerica's common stock edged up 12 1/2 cents a share to close at $39.50 in New York Stock Exchange composite trading.

Some analysts were cautious in their reaction to the announcement, saying they had little information about the deal.

''I don't know what to think. There's no information on Smith Barney since it's private,'' said W. Dudley Heer, a vice president of Chicago-based Duff & Phelps. ''It certainly is in financial services, which is Primerica's area of emphasis.''

Heer said Primerica has been ''very quiet'' during the last three months, and that Wednesday's announcement was the company's first major move since Gerald Tsai Jr. took over as chairman in January.

However, Tsai said the acquisition had been in the works for three years.

Tsai, formerly an aggressive stock analyst, was instrumental in taking American Can out of the can business and into financial services, a change in direction the company announced in 1981. Since 1982 the company has invested more than $1 billion into financial services.

''We are doing this because I believe financial services is global and it will be more so,'' Tsai said in an interview. ''The right way to go global is through investment banking. I think London and Tokyo and other countries are important for the future and we have no presence (there).

''Smith Barney is a very well-managed, conservative, well-capitalized company,'' Tsai said. ''We have mutual funds, we have insurance products, we have mortgage products we can offer to Smith Barney. They have 94 domestic offices and seven or eight offices outside of the country.

''They enjoyed a 25 percent compound growth in earnings over the last 10 years, and a return on equity in excess of 20 percent,'' he added.

The proposed alliance is the latest example of a decade-old trend on Wall Street in which closely held investment firms have sought additional sources of capital by merging, issuing stock to the public or selling minority stakes to institutional investors.

Last year, for instance, the investment firm Kidder, Peabody & Co. sold 80 percent of the firm to General Electric Co. for an estimated $600 million.

Smith Barney Chairman John A. Orb said in a statement that his firm was ''very excited about the prospect of joining forces with Primerica and its outstanding family of financial services companies.''

''Together our organizations will be better able to meet the challenges and opportunities in the rapidly changing international financial services marketplace,'' he said.