Schmidt is the third non-Australian to coach the Wallabies after fellow New Zealanders Dave Rennie, who was sacked to make way for Jones, and Robbie Deans, who was in charge from 2008 until the end of the 2013 Lions tour.
The 58-year-old will now go head-to-head with Andy Farrell, the man who replaced him as Ireland coach in 2009, when the Lions return next year under the direction of the Englishman.
Jones returned to great fanfare in January last year but the Wallabies won just two of nine tests in his second spell as Australia coach and the twice-world champions crashed out in the pool stage of the World Cup for the first time.
Schmidt said he shared Rugby Australia's desire to revive the Wallabies after a lean nine years, especially with the Lions tour being followed by the 2027 World Cup on home soil.
"I'm desperate for the Wallabies to be competitive, and if I can help I'm here, that's why I'm here. I think the global rugby family is desperate for the Wallabies to be where they need to be," he told reporters in Sydney.
"I do think it's also a little bit of a rebuild that will take a little bit of time. I'm probably a pragmatist, I can't promise anything other than I'll be working really hard to try to make it as successful as it can be."
Schmidt built his coaching reputation with Irish province Leinster and solidified it in six years as Ireland coach from 2013 to 2019.
He led Ireland to three Six Nations titles, including the 2018 Grand Slam, and to a first-ever victory over the All Blacks and a first test win against the Springboks in South Africa.
Schmidt joined Ian Foster's coaching team at the All Blacks in 2022 and was widely credited with the turnaround in their fortunes in the lead-up to last year's World Cup, where they reached the final.
Schmidt said Australian rugby fans should not read any lack of commitment into the length of his appointment in a game where coaches are usually contracted through the next World Cup.
"It's certainly not a hit and run," he added. "I think for both RA and myself, it just is a good fit at this time.
"If we get to the end of the British and Irish Lions series... and the discussion... is that the best thing is for me to stay, then that's a bridge we'll cross then."
Schmidt's first assignment will be a home July series against Wales, who thrashed Australia 40-6 at the World Cup last year to usher the Wallabies towards the tournament exit.
"(We'll be) trying to get some early wins on the board, and those wins may be just that we perform better, even if we don't quite get the outcomes we're looking for," Schmidt said.
"But I'm also a realistic coach. You're judged on your outcomes and you live or die by them."
