Cockerill, 52, was the only member of Eddie Jones' backroom staff still involved in the England set-up after Steve Borthwick replaced the Australian as head coach in December.
But the former Leicester and Edinburgh head coach saw his role reduced from being in overall charge of the pack to overseeing the worst performing scrum of any leading nation in a 2022 where England won just five out of 12 Tests.
A former England hooker, who won 27 caps from 1997-99, Cockerill was briefly interim head coach after Jones was sacked, having been brought onto the Red Rose staff by the veteran boss in September 2021.
Cockerill had hoped to be involved with England at this year's World Cup in France but said the lure of returning to a permanent post in the Top 14, where he was previously head coach of Toulon, was too strong to resist.
"It has been an honour to not only play for my country but to also get the chance to coach England," said Cockerill in an RFU statement.
"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.
He added: "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.
"I will continue to be fully focused on England and this Six Nations campaign, working with this group of players as they begin a new journey together."
Borthwick's reign as England started with a third successive Calcutta Cup defeat by Scotland in a Six Nations opener on Saturday, with the former Red Rose captain insisting the team he had inherited from Jones "weren't good at anything".
Nevertheless, Borthwick said Cockerill was "an excellent coach" and added: "It was a difficult decision for him to leave and he has our support."
England continue their Six Nations at home to Italy on Sunday.
Cockerill will take over at Montpellier, who are currently eighth in the Top 14, from Olivier Azam, under head coach Philippe Saint-Andre who welcomed the recruitment of a "world class coach".
"Richard is an experienced and well-rounded technician who will coach our pack in many areas of the game: line-out, scrum, ball-carrying and everything related to the forwards' game," the former France coach said in statement.
