Former ACT Brumbies coach McKellar was being groomed as Rennie's successor before the New Zealander was sacked in January and replaced by Jones, who was himself fired by England in December.
Steve Borthwick replaced Jones in the England role and, according to media reports, it is his former job at Leicester Tigers that McKellar is leaving Australia to fill.
"This was an extremely difficult decision to make but it's one that's made with my best professional and family interests in mind," McKellar said in a Rugby Australia statement.
"I firmly believe my next challenge will make me a better coach and hopefully allow me to return home and contribute in a positive fashion to Australian rugby in the future."
McKellar enjoyed success at the Brumbies with a forwards-based attacking style -- including a potent rolling maul -- that would make him a good fit at Leicester.
Rugby Australia had clearly hoped that McKellar would stick around until after this year's World Cup in France before making a move abroad.
"We are disappointed that Dan will not continue with the Wallabies this year," said chief executive Andy Marinos said.
Highly respected Australian coach Laurie Fisher last week announced his disappointment he would not be continuing as a Wallabies assistant under Jones.
Attack coach Simon Wisemantel, who worked with Jones in the England set-up ahead of their run to the final at the 2019 World Cup, quit the Wallabies for family reasons last year.
Media reports in Australia say that he has agreed to work on a consultancy basis with Jones ahead of this year's World Cup, which takes place in September and October.
"Together with Eddie we will continue to work hard to assemble a quality coaching staff to deliver a high performing environment in our preparation for the Rugby Championship and Rugby World Cup later this year," Marinos added.
