David Irving now faces an estimated £2m legal bill
He also now faces a bill for legal costs estimated at £2m.
Mr Irving had sued US academic Deborah Lipstadt and publishers Penguin Books for libel over a 1994 book.
He said Denying the Holocaust: The Growing Assault on Truth and Memory had destroyed his livelihood and generated waves of hatred against him.
After a four-week trial in April last year, Mr Justice Gray ruled that Mr Irving was anti-Semitic, a racist and an "active" Holocaust denier.
He also refused Mr Irving leave to appeal - and on Friday the Court of Appeal said he could not try to overturn this ruling.
Mr Irving was not in court for the announcement, instead said to be busy promoting sales of his new book on Churchill.
Bankruptcy threat
Lawyers for Penguin Books and Ms Lipstadt have been given more time to prepare a detailed assessment of their costs, estimated at £2m.
But the historian must now pay interim costs of £150,000 towards the final bill.
Richard Rampton QC threatened bankruptcy proceedings if the sum is not paid within three weeks.
Mr Irving, 63, who has a flat in London's Mayfair, brought his appeal with the help of donations from supporters - many of them from abroad.
At the original trial, Mr Justice Gray ruled that Ms Lipstadt was justified in what she had written.
He dubbed Mr Irving "an active Holocaust denier; that he is anti-Semitic and racist and that he associates with right wing extremists who promote neo-Nazism".
He said that the 63-year-old historian had, for his own ideological reasons, deliberately misrepresented historical evidence and portrayed Hitler in an unwarranted favourable light.
'Predictable' outcome
At the Court of Appeal, Lord Justice Pill, Lord Justice Mantell and Lord Justice Buxton said that Mr Justice Gray was "fully entitled" to these views.
Lord Justice Pill said: "We acknowledge that [Mr Irving] has over the years modified, and in some respects, significantly modified, his views upon some of the relevant events.
"However, the respondents were justified in describing him as 'one of the most dangerous spokespersons for Holocaust denial'."
Mr Irving had expressed doubts about whether there had been mass gassing at the Auschwitz concentration camp.
Lord Justice Pill said: "No objective, fair-minded historian would have serious cause to doubt that there were gas chambers at Auschwitz and that they were operated on a substantial scale to kill hundreds of thousands of Jews".
Solicitor Mark Bateman, for Penguin, said "The only comment that we can make is that it is a very predictable outcome.
"It is a shame that we have been dragged through the Court of Appeal when there was really no issue in Mr Justice Gray's judgment - his judgment was sound."