Hatley arrived at the Recreation Ground in the wake of last autumn's World Cup and his initial duties overseeing the forwards and defence have been swapped for the main tracksuit role under director of rugby Stuart Hooper.
The former England Saxons prop was appointed England scrum coach by Jones in 2016 and follows in the footsteps of Paul Gustard and Steve Borthwick, who have been appointed to similar positions at Harlequins and Leicester respectively.
"Neal's ability to connect with the players and develop those relationships, along with his ability to deliver the key principles of our play, is a huge skill," Hooper said.
"He takes players on the journey and helps them understand why we do what we do.
"His ability to connect with those guys, influence them, develop them outside of the training field is massive and an absolutely fundamental part of being a head coach."
Hatley made 193 Premiership appearances before beginning his coaching career as an academy manager at London Irish.
"As head coach, I'm responsible for field performance. With my focus on delivering great performances on the pitch, it allows Stuart to focus on how we want to play and perform," Hatley said.
"I want to make sure I get the best out of our players and that's a lot about building relationships, knowing they trust your leadership.
"I've set out very clearly how I expect our players to behave, how I expect them to train and how we expect to treat each other."