Jones quit his native Australia after leading them to a dismal showing at the Rugby World Cup, and repeatedly denied reports that he was set to take over in Japan.
Australian media had reported that the 63-year-old had interviewed for the job during the Wallabies' World Cup campaign in France.
Jones's appointment on Wednesday sparked a furious reaction in the Southern Hemisphere, with former All Blacks great Sonny Bill Williams branding the coach "a disgrace".
Jones said he did not regret his actions, telling reporters "it sits well with me".
"I wish Australia all the best," he told a packed press conference in Tokyo.
"I feel terrible about the results, because I wanted to go back and change Australia.
"But I don't feel any guilt at all about this process."
Jones repeated his claim that he had not interviewed for the Japan job until December.
He said his online meeting with a recruitment company shortly before the World Cup was to "share my experiences of Japan".
Jones said "everyone is entitled to their own opinion" but he did not feel the need to apologise to Australian fans.
"The only thing I can control is what I did, and it sits well with me -- I don't have a problem with it," he said.
"If people feel like that, that's their judgement. I can't control that."
Jones quit the Wallabies after two wins from nine Tests since taking over in January, including a worst-ever World Cup performance where they failed to make it out of the pool phase.
His insistence on fast-tracking rookies at the expense of veterans badly backfired in high-pressure games, as did a revolving door of unproven captains.
Japan identity
Jones will officially begin his second stint in charge of Japan on January 1.
He previously coached them for three years from 2012 and led them to their historic win over South Africa at the 2015 World Cup.
Jones said his aim was to turn Japan into a team "that has a real identity".
"Any great team in any sport, it doesn't matter what shirt they play in, you can see clearly the team that they are," he said.
"I think we need to develop that with Japan, so that's going to be one of the major focuses going forward."
Under Jones, Japan stunned South Africa 34-32 in a match that became known as the "Miracle of Brighton".
That was only Japan's second win at a World Cup, and they also went on to beat Samoa and the USA that year before exiting at the pool stage.
They reached the quarter-finals on home soil in 2019 under Jones's successor Jamie Joseph, but exited at the group stage at this year's tournament in France.
Jones targeted a return to the World Cup knock-out round in 2027 and said Japan "need to play the game faster than the opposition".
He also said South Africa's diminutive World Cup-winning winger Cheslin Kolbe, now playing in Japan for Tokyo Sungoliath, could be an inspiration for his players.
"He's as strong as an ox, he's as fast as a cheetah, and he's as elusive as a ninja -- that's how Japanese players can be," Jones said.
"He's a fantastic example, so what we want to find is players who can be like him, and they're out there."
