President Reagan yesterday announced that he will nominate Charles C. Cox, 38, now chief economist of the Securities and Exchange Commission, as a commissioner, succeeding Republican John Evans, who is widely regarded as a champion of small investors and small businessmen.

In deciding an issue that has created controversy within the securities industry for the past several months, Reagan ignored the conclusion of four out of the five existing SEC commissioners--two Republicans and two Democrats--that Cox is not qualified for the SEC post, according to sources.

Cox's sole supporter on the commission was its chairman, John S.R. Shad, who had hand-picked him a year ago for the SEC's chief economist's job, and recommended him to Reagan for the promotion.

Shad, who came to the SEC from the Wall Street firm of E.F. Hutton & Co., seeks to build an SEC majority that will help him carry out his campaign to hasten deregulation within the securities industry.

Evans' supporters said that the 50-year-old commissioner had a proven record as a conservative deregulator. He led the fight to get rid of fixed commission rates, making it possible for small investors to buy and sell stock at a discount.

Evans had sought reappointment with the backing of an influential bipartisan group of senators, and has told friends that Shad told him that he wouldn't oppose him.

Two of the other commissioners, Republican James Treadway and Democrat Bevis Longstreth (both Reagan appointees), told Shad directly that they thought Cox unfit for the job, sources said. They reportedly said that Cox's lack of legal and technical experience was disturbing, and that his training in macro economics had no real relevance to the law enforcement role of the SEC.

Authoritative sources said that a similar low opinion of Cox's aptitude and suitability for the job is held by commissioner Barbara Thomas, a Democrat. Cox's fourth opponent, of course, is Evans, originally named to the SEC by Nixon in 1973, and reappointed by Carter in 1978. His term actually expired on June 5, 1983.

Cox got his Ph.D. in economics at the University of Chicago, taught at Ohio State for eight years, and two years at Texas A&M before arriving at the SEC last year.

In nine months at the SEC, his views, expressed in internal memoranda, appear to have generated the opposition of the other commissioners and many influential members of the SEC staff.

Disapproving SEC staff members have kept up a drumbeat of opposition to Cox, noting, among other things, that he never achieved tenure at Ohio State. In a telephone interview yesterday, Cox acknowledged that this is so, but protested that his untenured status was the result of not meeting the frequency test for publication, and did not reflect on the quality of his work.

But a critic insisted, "The chairman plucked Cox out of Texas A&M, and made him chief economist. I'm afraid that as a commissioner, he'll be totally beholden to Shad, a rubber stamp."

But Cox was given high marks by George J. Stigler, a professor who published some of Cox's research when Stigler was editing the Journal of Political Economy, and by Edward John Ray, head of the Economics Department at Ohio State when Cox was an assistant professor there.

Stigler said Cox "is a highly qualified professional economist", one who "has a full command" of both economic theory and of methods of analysis.

Ray said that Cox is "one of the brighest young economists I have known", and is "uniquely qualified" to deal with the issues at the SEC.

Over the past several months, Evans was backed for reappointment by his two home state senators, Utah Republicans Orrin G. Hatch and Jake Garn, the Senate Banking Committee chairman, and by the National Association of Small Businessmen.

But earlier this week, the White House persuaded Garn to abandon his fight for Evans and agree to support Cox when the nomination goes to the Banking Committee, sources said.

Opponents of Cox at the SEC have argued that he is an academic economist with no background in securities, and no experience in business and finance.

In an interview yesterday, Cox challenged critics who question his competence. He said his principal work is in micro economics, with specialties in industrial organization and "analyzing the economics of government regulation" which could have special relevence to the SEC.

Shad, who said Cox was picked "by the White House out of a pack of outstanding candidates," said that Cox's economic background would be of great help "in one important aspect of the commission's work--sensitivity to the cost-effectiveness of securities rules and regulations."

Shad clearly is anxious to have his own team. He and most of the other commissioners have been at odds over many issues during the past year. All of the others opposed Shad's acquiescence in the Reagan budget for the SEC, which beginning Oct. 1 will force additional cuts in the staff.

But Evans' policy differences with Shad have been especially pronounced. For example, they have been on opposite sides of the "national market" question. Evans would like to see a computerized trading system that would make it easier and possibly cheaper to buy securities, but this would hit hard at the New York Stock Exchange's preeminent role. Shad supports the exchange's side of the issue. Shad and Evans also differred on how tough the SEC should be on insider trading.

In marked contrast to Evans, critics said, Cox during the past year on the SEC staff showed little sensitivity to the problems of the individual investor. In a private SEC staff memorandum dated Oct. 28, 1982, Cox said that it is obvious that professional investors have an advantage over small investors, that there is nothing wrong with that, and that it is reasonable that things should continue that way.

"The charge that I am not concerned, or that I have very little regard for small investors is just completely unfounded," Cox said.

When the question of Evans' reappointment came up in 1978, Wall Street launched a vigorous, and almost successful campaign against him, and Carter took almost a year before deciding to send his name up again.

A Cox appointment, critics said, followed by the departure of Democratic Barbara Thomas, who announced her resignation last month and will depart this fall, will tilt the commission solidly toward the securities industry.

The term of the other Democrat, Bevis Longstreth, expires in June, 1984.