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The unprecedented transition of power under the 25th amendment officially occurred when Mr Nixon handed a letter of resignation to Secretary of State Dr Henry Kissinger at 1135 local time (1635 BST).
He announced his departure last night in the face of an imminent impeachment trial - and possible removal from office - over the Watergate affair.
Mr Ford became the first president to come into office without a single vote being cast in his favour.
Speaking only minutes after taking the oath of office in the East Room of the White House, he said: "You have not elected me as your president by your ballots. So I ask you to confirm me as your president with your prayers."
'Open and candid'
The Republican promised an "open and candid" administration, declaring that at the age of 61 he was too old to "change his habits."
Turning his back on the Watergate era, he said: "Truth is the glue that holds our Government together. Not only our government but civilisation itself.
"That is unbroken at home and abroad. I expect to follow my instincts of openess and candour with full confidence that honesty is always the best policy in the end."
The new president called for an immediate joint session of Congress on Monday evening to discuss the "priority business of the nation."
He appointed a well known Washington reporter Jerald terHorst as his press secretary in place of Ron Ziegler, who left with Mr Nixon.
Mr Ford had publicily indicated that he would not be welcome in his White House.
Earlier the new president announced that Dr Kissinger would retain his position as secretary of state.
He has already begun meeting ambassadors to give assurances of the foreign policy continuity Mr Ford declared in his speech.
The new president stated: "To the peoples and the governments of all friendly nations, and I hope that could encompass the whole world, I pledge an uninterrupted and sincere search for peace."
Mr Ford has been the Republican congressman for the Grand Rapids district of Michigan but was more recently the Republican minority leader in the House of Representatives.
He became vice president under Mr Nixon last November when Spiro Agnew resigned after pleading guilty to tax evasion.
Meanwhile, Mr Nixon has flown to California with his wife, daughter Tricia and her husband following an emotional farewell meeting with the Cabinet and White House staff.
Earlier it was officially announced that he had granted no pardons to anyone before his presidency expired.
President Ford served just over two years in office before he lost to Jimmy Carter in a closely-fought election in November 1976.
He arrived at a difficult time when the government was still embroiled in accusations of corruption in the wake of the Watergate scandal.
The American public reacted angrily when he formally pardoned former US President Richard Nixon just two months after coming into power.
After that President Ford's reputation never recovered and within a year of coming to power he survived two assassination attempts in the space of 17 days.
But he did manage to prevent Israel and Egypt from starting a war in the Middle East when he persuaded the two countries to accept an interim truce agreement.
He launched a successful business career after he stepped down but this was eventually overshadowed by his wife Betty's new drug rehabilitation clinic for the rich and famous.
Mr Ford continued to speak out on important political issues.
He survived two mild strokes at the age of 87 at the Republican Party convention in 2000. He died in December 2006. President George Bush paid tribute to him as the man who came along when America "needed him most".
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