Jones handed in his resignation in August, only seven months after joining the England set-up from Rugby World Cup-winning South Africa.
The loss of the highly rated Jones came “out of the blue” and was “deeply disappointing”, according to Rugby Football Union chief executive Bill Sweeney.
Jones has a 12-month notice period as part of his contract and is expected to continue as part of the England coaching set-up, working remotely to provide tactical analysis.
El-Abd has a long relationship with Borthwick, with the pair sharing a flat during their days at Bath University in the early 2000s.
While Borthwick progressed to become a mainstay of the Bath pack, El-Abd built his career at Bristol before moving crossing the Channel to play for Toulon and Oyonnax.
As a forwards and defence coach El-Abd helped Oyonnax to the second-tier Pro D2 title in 2013 and Champions Cup qualification two years later.
He filled the same role at Castres for four years – a spell that included a 2018 Top 14 title – before returning to Oyonnax as director of rugby in 2019.
Under his leadership the club were promoted back to the Top 14 in 2023, but suffered an immediate return to Pro D2 last season, winning seven of 26 games.
“Joe’s knowledge, passion for the game, and proven experience in developing high-performing teams, will be key to the squad’s ongoing development,” said Borthwick.
“Joe embodies the qualities we value in the England rugby team and am I sure he will add to our environment and quickly deliver continued improvements to our game.”
Oyonnax president Dougal Bendjaballah had insisted he would not allow El-Abd to leave his current post before next summer and has delivered on his promise.
Oyonnax are currently midtable in Pro D2 after two wins from four games.