Jones will leave the Springboks after the autumn's Rugby World Cup, before joining England’s ranks on the turn of the year.
Former Ireland full-back Jones spent three years coaching with Munster before moving into South Africa's backroom staff.
The 35-year-old has developed a big reputation for the quality of his coaching, having helped South Africa claim World Cup glory in Japan in 2019.
“Our immediate focus is on preparation for the Rugby World Cup 2023, we are continuing to build our programme to be in a position to compete to be world champions once again," said England boss Borthwick.
“At the same time, I also want to ensure we are preparing for long-term success for this England team and I am excited that a coach as talented as Felix is joining next year.
“Felix has been competing at the top of world rugby during his four years with South Africa and will bring invaluable experience to our set-up.”
Jones will link back up with Aled Walters at England, with the pair having worked together with the Springboks.
Walters will join England from Leicester this summer as head of conditioning, with Richard Wigglesworth another addition to the Red Rose set-up from the Tigers.
“Like with Aled Walters, Felix was an integral part of the team that won the Rugby World Cup in 2019," said Borthwick.
“Together with Richard Wigglesworth and Kevin Sinfield, we are putting in place a coaching team who have spent their careers at the highest level competing for trophies. That is exactly what we want for this England team."
England are still seeking a forwards coach to replace the departing Richard Cockerill.
Saracens' Ian Peel has been the frontrunner for that role for some time, but the StoneX Stadium club have also been hopeful of retaining one of their top off-field talents.