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His rival President Gerald Ford conceded victory at a news conference in the White House press room at midday. It is the first time since 1932 a sitting president has been dismissed from office.
The president had lost his voice through campaigning and had to ask his wife Betty to read a telegramme of congratulation.
It has been a nailbiting finish to what has generally been regarded as a rather dull campaign.
Mr Carter claimed victory for the Democrats shortly after dawn in Atlanta but a Republican demand for the impounding of the New York State voting machines seemed to place the result in question.
Any doubt was finally lifted when New York returned a substantial majority for Mr Carter and President Ford made his concession speech.
The final results show Mr Carter won 51% of the popular vote, three points ahead of Mr Ford. He gained 297 of the vital electoral college votes against Mr Ford's 241.
Despite the closeness of the race, the country is overwhelmingly under Democratic control. In the Senate the Democrats hold of a lead of 61-38. They hold the House of Representatives by 290-145.
Record turnouts were reported in many areas as Americans flocked to the polls, keen for a change in government.
Interviews conducted with people leaving polling stations suggested Mr Carter had attracted a big following among Roman Catholics. It had been assumed his strong Baptist beliefs would alienate the Catholics.
He also appeared to have strong support among blacks and young people.
The politician, who emerged from the relative obscurity of a peanut farm in his native Georgia to run for the presidency, appealed to voters with his slogan "Trust me".
Commentators say Mr Ford and the Republicans were still suffering from the damage caused by the Watergate scandal and the President's decision only two months later to pardon Richard Nixon.
Early results saw Mr Carter take the lead, winning the key industrial state of Pennsylvania and all the southern and border states.
President Ford took states in the East and Mid-West but even his home state of Michigan looked a bit doubtful after a Democratic Senate candidate Ronald Riegle won his seat despite a personal scandal.
President Carter lasted one term in office before being swept out of power by Republican Ronald Reagan.
He will be remembered for two major achievements; the signing of the Panama Canal treaty, under the terms of which the waterway was transferred to Panama's control in 1999, and also for the Camp David agreement in 1978 which led to peace between Egypt and Israel.
However, his decision to allow the deposed Shah of Iran to escape to the US in 1979 led ultimately to the Tehran hostage siege, which only ended with Ronald Reagan's election as president.
After leaving office, he founded the Carter Centre, based in Atlanta. Under its auspices he has worked as an international mediator in various of the world's trouble spots including Ethiopia, Haiti and Bosnia.
The Centre has also established health programmes which have all but eradicated Third World diseases like guinea-worm and it is also tackling river blindness.
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