Great Britain won gold medals at the London 2012 Olympic Games in both men's and women's team pursuits – two of seven gold medals claimed on the capital’s track last summer.
But following a coaching restructure Manning moves across from his successful tenure as women's endurance coach to take up the same role with the men.
This means Manning will now be responsible for the men's team pursuit, among other endurance disciplines, while Newton will replace him as women’s endurance coach.
Keith Lambert will replace Newton to coach the GB men's endurance academy riders on the road, while head coach Shane Sutton will continue to oversee GB track coaching as a whole.
"We've got a fantastic track record in the team pursuit and we have accumulated a wealth of knowledge of the discipline over previous Olympic Games," said British Cycling performance director Sir David Brailsford.
"As the UCI have changed the women's team pursuit event to four riders over four kilometres just like the men, it seems the perfect time for us to pool all this knowledge in order for the endurance riders to continue to perform optimally.
"In both Chris and Paul we have experienced and successful coaches who have also both competed themselves at Olympic level in the track endurance disciplines and I'm confident they can continue to move us forward as we progress along the road to Rio."