Connacht's Paul Bunce will replace Bennett at Bristol in the summer.
Bunce has worked alongside the Pro12 club's current boss Pat Lam - who will join Bristol as their new head coach from June - for the past three seasons.
Bennett has been with Premiership strugglers Bristol since 2014, helping them win promotion last season.
Reporting to the RFU's professional rugby director Nigel Melville, Bennett will manage all performance staff and services for the governing body, leading on aspects such as anti-doping and nutrition.
Bennett played for Swansea, Cardiff and before moving into fitness work that has involved stints with Scarlets, Celtic Warriors, Wales, Ospreys and Bristol.
He was on Wales' fitness staff when they won Grand Slams in 2005 and 2008.
Bunce was previously head of strength and conditioning at Bath and Welsh region Newport Gwent Dragons.
Bristol's interim head coach Mark Tainton told the club website: "Paul has a wealth of knowledge in his field and a proven track record of driving the physical preparation standards of professional teams.
"The style of rugby that Pat wants his team to play is high-tempo and full of energy. Paul - with his background and experience - is well equipped to deliver those goals."
Bristol's head of performance Mark Bennett is to leave at the end of the season to join the Rugby Football Union as head of sports science and medicine.