After days of listening to frank, negative appraisals of his late-starting prospects, former president Gerald R. Ford announced yesterday that he will not be a candidate for the 1980 Republican presidential nomination.

"America needs a new president," Ford said in a statement he read to reporters outside his office at Rancho Mirage, Calif.

". . . I have determined that I can best help that cause by not being a candidate for president, which might further divide my party. I am not a candidate. I will not become a candidate.I will support the nominee of my party with all the energy I have."

With that, Ford ended one of the more unusual odysseys of modern presidential politics. For weeks, Ford had made it clear that he wanted very much to run for the office he once held. He had clearly become frustrated sitting on the campaign sidelines and watching Ronald Reagan, his 1976 GOP adversary and still probably the least favorite of his fellow Republicans, pile up a large front-runner's lead.

On March 1, in an interview with Adam Clymer of The New York Times, Ford pointedly said that Reagan cannot win a presidential election even if he becomes the nominee. And he invited leading Republicans to urge him publilcy to enter the campaign, even though many primary deadlines had already passed.

But the response of the Grand Old Party brought mostly "surprises" and "disappointments," Ford later admitted. Those who had urged him to run privately would not do so publicly. Most of his close political associates told him the delegate numbers were stacked against him. It was too late. He could not win.

And so Ford stood yesterday in a gray suit and tie in the California sun, with his wife at his side, and announced what he called "a final and certain decision." He said his wife agrees with his conclusion. And he added: "It has been the toughest decision of my life, because I believe our country is in very deep trouble."

But while Ford's announcement ended this unusual up-again, down-again political odyssey -- one that confounded even some of the most experienced and well-rounded of political observers -- it left Ford with a rather awkward problem of political logic still unexplained.

He has said that America needs a new president, yet he has also said that the Republican front-runner, Reagan, cannot win in November. The unanswered question, then, is just how Ford believes that his noncandidacy will help bring about the defeat of President Carter and election of a new president, which Ford said yesterday was "more important than anything else."

Both George Bush and John B. Anderson had been most unhappy with Ford's efforts in the past couple of weeks to marshal public support for his candidacy. They felt he was trying to pull his support from middle-of-the-road Republican elements that otherwise would have been theirs. Bush especially had maintained that a number of top-level Republicans had withheld endorsements from him until Ford made his decision known.

Ford chose to make his announcement before Tuesday's important Illinois primary election, a factor not lost on those who are in the state and running for president.

Bush, Anderson and Reagan were quick to issue statements yesterday welcoming Ford's decision. The grin on Reagan's face told the story, but his words appeared low-key. "It clears the air of a lot of uncertainty," he told reporters in Rock Falls, Ill., where he is campaigning for the Illinois primary next Tuesday. "I'm glad a decision has been made."

Bush's statement was subdued, short on expressions of personal pleasure and long on expressions of respect for the former president.

"I know this is not an easy decision for the president," Bush said in a statement issued by his office. "It does clear the air politically . . . . I have great respect for Gerald Ford. I have consistently said that if he got involved it would complicate things politically for me because we do have similar views on many things."

Anderson, speaking at a news conference in Champaign-Urbana, Ill., was more euphoric. He called Ford's decision "a positive development for my campaign." And he added: "Very frankly, I am, of course, pleased that the president will not enter the contest. I respect and admire him greatly . . . perhaps some of the votes that would have gone to him will now come to me."

Ford made his decision public after one last conference in Rancho Mirage with some of those who have been close to him. Attending that two hour session in Ford's office were Thomas Reed, the former Air Force secretary who had just formed a draft Ford committee; Alan Greenspan, Ford's former chief economic adviser; John Marsh, a former White House assistant; Stuart Spencer, Ford's chief campaign tactician in 1976; political consultants Doug Bailey and John Deardourff, and his personal aide, Robert Barrett.

But in fact Ford had heard most of the candid, often negative advice that his inner circle had to offer. Ford met in Washington Wednesday with most of those advisers, plus his former White House chief of staff, Richard Cheney, now a congressman from Wyoming. And that session produced divided opinion on whether Ford should try to make the late run -- but unanimous agreement that the race would be difficult, at best.

Yesterday, after Ford's statement, Draft Ford Committee spokesman Larry Speakes pronounced his newly founded committee's work ended. He added: "About all we have is a phone bill to pay."