The Israeli ambassador Dror Zeigerman said: "I hope it will stop those who are continuing to try to deny the Holocaust - continuing with their behaviour which is racist and anti-Semitic.
The judge found in favour of Professor Deborah Lipstadt, telling Mr Irving he was an active Holocaust denier, anti-Semitic, racist and associated with right wing extremists who promoted neo-Nazism.
"Let us remember that this trial was not about whether the Holocaust happened, but whether I was correct in describing David Irving as a denier of the Holocaust, anti-Semitic and a right-wing extremist.
"The judge has found that I was correct on all these points.
"I see this not only as a personal victory, but also as a victory for all those who speak out against hate and prejudice."
Prof Lipstadt added: "There is no end to the fight against racism, against anti-Semitism, against hatred.
'Hugely expensive'
"We just have to fight every battle - but this was a major battle."
Penguin said Books said it had been a "hugely expensive" case and it would be left significantly out of pocket even after taking active steps to recover its costs.
The Israeli ambassador Dror Zeigerman said: "I hope it will stop those who are continuing to try to deny the Holocaust - continuing with their behaviour which is racist and anti-Semitic.
"The lesson for the new generation - my generation - is that we have to continue the struggle."
Eldred Tabachnik, QC, president of the Board of Deputies of British Jews, said: "The decision proves that David Irving is a falsifier of history.
Lord Janner of Braunstone QC, chairman of the Holocaust Educational Trust, said: "It is an epic victory for truth and justice.
"The Irving case shows the crucial importance of educating our young people in the tragedy of the Holocaust especially as a symbol of the dangers of allowing racist dictatorships to rule."
The Simon Wiesenthal Centre, a movement dedicated to victims of the Nazis, said the verdict was a "victory of history over hate".
"David Irving's career as a historian is over," the centre said in a statement.
"Today's decision definitely places Irving where he belongs - not as a historian, but as a leading apologist for those who seek to whitewash the most heinous crime in human history."
Emeritus Professor Donald Cameron Watson, of the London School of Economics, who worked with Irving in the 1960s, told the BBC Mr Irving's claims over the holocaust had been "ridiculous".
'Weird theories'
He told BBC News 24: "The evidence is overwhelmingly against him.
"It's ridiculous. It's on a par with creationism and some of these other weird theories that have some public support."
Mr Irving has an outstanding libel action against The Observer newspaper and writer Gitta Sereny, who made similar claims about him to those of Professor Lipstadt.
Roger Alton, editor of The Observer, said: "This ruling is an absolute vindication for the paper's coverage of Irving's career. In the event that David Irving does not withdraw his claims against The Observer we will be applying for the case to be struck out.
"In either case we will be asking Irving to pay our costs. It would be a huge waste of time and money for the same issues to be litigated again."