Both the people he replaced had resigned from their posts without serving full terms, requiring someone to take their place until the next election... firstly Spiro Agnew resigned as Vice-President in 1973, and the Senate and House of Representatives voted Gerald Ford to replace him when Richard Nixon proposed him (so he was elected after a fashion, although not directly by the public). Then the next year the Watergate scandal hit the fan and Richard Nixon resigned, so Ford leapt all the way up to the President's office, as is laid down in the constitution. (Sorry, I don't know why Spiro Agnew resigned as VP, hopefully someone else can fill in that blank) edit - I looked it up, Spiro Agnew was charged with tax evasion in 1973.

That is really a very intriguing question. Consider who it was that gave him that job as VP, Richard Nixon. Consider too that one month after Nixon resigned, he was pardoned by Ford. Obviously a deal was worked out before Ford was made VP. One final thought regarding Mr. Ford. He was a member of the Warren Commission that was assigned to investigate the assassination of J.F.K. "According to Jim Marrs, author of Crossfire: The Plot That Killed Kennedy (1989), at pp. 466-67: many Kennedy assassination researchers consider Gerald Ford to have been the FBI’s “spy” on the Warren Commission. This was confirmed by a memo from Cartha DeLoach, a close aide to FBI Director, J. Edgar Hoover, in which DeLoach noted: “I had a long talk this morning [December 12, 1963] with Congressman Gerald R. ‘Jerry’ Ford . . . He asked that I come up and see him . . . Ford indicated that he would keep me thoroughly advised as to the activities of the Commission. He stated this would have to be on a confidential basis, however, he thought it should be done. He also asked if he could call me from time to time and straighten out questions in his mind concerning our investigation. I told him by all means he should do this. He reiterated that our relationship would, of course, remain confidential.” Marrs quotes former New Orleans District Attorney Jim Garrison, the only prosecutor to bring criminal charges related to the Kennedy assassination and the subject of director Oliver Stone’s movie, JFK: “Ford [also] enjoyed the reputation of being the CIA’s best friend in the House of Representatives.” According to Marrs: “Ford’s name as a member of the Warren Commission was recommended to President Johnson by Richard Nixon. A World War II Navy veteran, Ford became the Commission’s most industrious member, hearing seventy out of the ninety-four witnesses who actually met with commissioners." Marrs reports that Ford "also profited from his time on the Commission. Ford had his first campaign manager and former Nixon for President campaign field director John R. Stiles hired as his special assistant. Ford and Stiles went on to write Portrait of the Assassin, a book that presented selective evidence of Oswald’s guilt." Marrs claims that Ford used classified Top Secret Warren Commission material in his book, and that Ford effectively perjured himself about during confirmation hearings for his appointment as Vice President before the Senate Judiciary Committee in 1973. Ford apologized and said that he had not attempted to mislead the committee. He was confirmed, sworn in as Vice President, and eventually became the nation's first unelected president". Sources cited, some info here from Wikipedia