He will take the same position at French club Montpellier.
Cockerill was the only remaining assistant coach from Eddie Jones' (63) reign after Steve Borthwick (43) succeeded the Australian as head coach in December.
Matt Proudfoot (51) left the England coaching team along with Brett Hodgson (44) and Danny Kerry (52) in January, and attack coach Martin Gleeson (42) also departed.
"It is disappointing not to work with Steve and the wider team beyond the Six Nations. I had hoped to be able stay for the Rugby World Cup, but the timings weren’t meant to be," Cockerill said.
"It has been an honour to not only play for my country but to also get the chance to coach England.
"Having coached and played in France previously, my family and I always had aspirations to return. This opportunity presented itself some time ago and it was too hard to turn down personally and professionally.
Later in the day, England also announced that Richard Wigglesworth (39) and Aled Walters will join their coaching setup ahead of the Rugby World Cup.
Wigglesworth has played international rugby for England as scrum half, with both joining from Leicester Tigers' backroom staff.
"Richard and Aled are two outstanding coaches in their fields who I know very well," said Borthwick. "Richard has been a proven winner throughout his playing career and has carried this into his coaching career.
"He already has international coaching experience from the 2019 Rugby World Cup, alongside a hugely successful playing career, and has amassed a wealth of knowledge. Few people have such an in depth, wide-ranging view and understanding of the tactical element of the game.
England take on Italy in the Six Nations this weekend, looking to bounce back from their opening day defeat to Scotland at Twickenham.
