President Reagan announced yesterday that he has appointed Paul A. Volcker to a second four-year term as chairman of the Federal Reserve Board and declared that Volcker is "as dedicated as I am to continuing the fight against inflation."

Climaxing weeks of speculation, Reagan disclosed what may be his most important economic decision this year in two short paragraphs at the opening of his regular Saturday radio broadcast.

Senior administration officials said the president had reached a private understanding with Volcker last week to pursue the anti-inflation battle, but not at the expense of inhibiting the economic recovery with high interest rates.

"They see eye to eye on this," said one official.

"Like the president, Volcker wants the recovery to be sustained and is committed to lower rates of interest," Treasury Secretary Donald T. Regan said yesterday.

The appointment won wide praise, and Volcker is expected to win easy confirmation by the Senate.

"Mr. Volcker has done an outstanding job at the Federal Reserve, and his continuation in that office is certainly in the best interests of the country's economic future," said Arthur Levitt Jr., chairman of the American Stock Exchange.

Sen. Thomas F. Eagleton (D-Mo.), in the Democratic response to Reagan's address, said, "I vigorously support" the reappointment.

In making the announcement, Reagan praised Volcker's "unquestioned independence." That independence was a concern in White House discussions of the reappointment.

A senior administration official said the president "is taking a risk here. This is the guy who a lot of people think wrecked Jimmy Carter." Attempting to control soaring inflation in late 1979, Volcker put into place policies that induced high interest rates and a recession going into the 1980 presidential campaign.

The administration official added that despite warnings from advisers that Volcker could take an independent course during next year's presidential campaign, Reagan went ahead with the reappointment.

In the Reagan administration, Volcker has become a symbol of both a largely successful effort to control inflation and a tight monetary policy that produced high interest rates and the worst recession since World War II.

Inflation was running at an annual rate of 13 percent when Volcker was first appointed in 1979, and is now at about 4 percent. But the drop in inflation came at the cost of the worst recession and highest unemployment since World War II, which together constitute one of Reagan's greatest political liabilities.

While the tall, cigar-chomping Volcker exerts strong influence over the nation's money supply, interest rates and general economic health, White House polls show that he is little known to most Americans and that they attribute the nation's economic situation to the president and Congress.

Reagan told aides of his decision Friday afternoon but decided against announcing it immediately because of its possible impact on the financial markets. Instead, he wrote and inserted the announcement in his speech, expressing concern to advisers that the announcement would leak out if he waited until next week.

Saying he had a "news flash" in the tradition of movies with reporters who yell into the phone "Give me the city desk, I've got a story that'll crack this town wide open," Reagan told his listeners: "Well I'm not wearing a hat or clutching a phone. But before getting into today's broadcast, I'd like to make an important announcement . . . . "

White House officials said yesterday the president had no commitment from Volcker to serve less than the four-year term. Volcker had said that he believed it would take 18 months more to deal with the continuing international debt crisis, leading to speculation that he might make a deal with Reagan to resign before the expiration of his second term.

In addition, Volcker is a Democrat, and some of Reagan's advisers doubted whether he would be willing to work closely with the White House during an election year.

In accepting the reappointment, Volcker did not indicate whether he would serve an abbreviated term. A statement issued from New York said, "I look forward to continuing to work with the president and Congress toward our common economic objective . . . . I do believe we now have a rare opportunity to achieve sustained growth on a firm foundation of stability."

The low-key manner in which Reagan made the announcement--calling Volcker only an hour before he went on nationwide radio and not appearing with him in the White House, a traditional practice with new appointments--was taking a page out of history.

Administration officials checked newspaper clippings to learn how President Lyndon B. Johnson had announced the reappointment of Federal Reserve Chairman William McChesney Martin at a time when Johnson and some members of Congress were not entirely satisfied with Martin's handling of monetary policy.

They discovered that Johnson had issued a routine personnel announcement and had not appeared with Martin.

The first administration discussions about the Volcker decision date back to the weeks before the late-May Williamsburg economic summit. Regan, who played an influential role in advising the president, told Reagan at the time that he should not rush into a decision on Volcker's future until after the summit. Volcker's term expires Aug. 5, officials said.

Meanwhile, the White House staff was instructed to produce a list of alternate candidates. At first Reagan's economic and political advisers were sharply divided over whether Volcker should be given another term. But in the end, according to several informed sources, none of the other candidates seemed a better choice than Volcker. White House counselor Edwin Meese III said the final decision for Volcker was unanimous.

"A key factor was the confidence Volcker enjoys in the domestic and international financial community," said an administration official. "He has established his independence and he would not have to show it" once Reagan reappointed him. There was concern among several advisers that any other nominee besides Volcker would try to demonstrate independence from the administration.

On the other hand, some administration officials thought that Reagan should have his "own man" running the nation's central bank. The leading alternative choice among these officials was New York economist Alan Greenspan, chairman of the Council of Economic Advisers in the Ford administration. But while Reagan had a private meeting about the job with Volcker, officials said he did not discuss it with any other candidates, including Greenspan.

Treasury's Regan was frequently critical of Volcker over the last two years. At one point he favored the appointment of economist Paul McCracken to the Fed post. But Regan spoke favorably of reappointing Volcker at a meeting with Reagan June 6, saying Volcker was "the right man at the right time," one official said.

Although the nation's money supply recently has been far above the targets set by the Fed, raising concerns in the administration about a resurgence of inflation, that was not a factor in Reagan's decision, another official said. "Reagan's decision was based on 2 1/2 years, not 2 1/2 weeks," the official said.