Snowball worked as head of sport for the London 2012 organising committee (LOCOG) and he will head up the division responsible for staging the 2015 Rugby World Cup.
Jevans, who has only been in the job since October 29 after she too was recruited from LOCOG, has divided the organisation into two departments - rugby operations and business operations. The restructure means there is no place at ER2015 for Ross Young, the chief operating officer who has worked on the delivery of the last three Rugby World Cups.
Young has left ER2015 with immediate effect along with marketing and communications general manager, Jon Duckworth. The recruitment of a director-level replacement for Duckworth has begun.
Jevans said: "The Rugby World Cup draw on December 3 marked a step-change for ER2015, from a planning to an operational phase.
"ER2015 needs a structure that reflects that change and ensures more direct focus on the delivery of the tournament, clearer reporting lines and accountability, and better defined business operations that reflect our changing priorities.
"Neil Snowball did a fantastic job as head of sport operations for LOCOG and he was responsible for the sporting operational framework which delivered the Games.
"He managed a multi-million pound budget and oversaw the delivery around venues, training bases, team liaison and all of the logistics that support such a huge undertaking."
Snowball's arrival continues the overhaul of ER2015 leadership, which began when Andrew Coslett replaced Martyn Thomas as chairman, initially on an interim basis, in December.
Since then, Jevans has been brought in from LOCOG to replace Paul Vaughan as chief executive and she has acted quickly to restructure the business and recruit Snowball.