The review will see the Trust's media relations work fall under the remit of its incoming head of policy Lee Elliot Major.
Evans reported directly to the Trust's director Michael Dexter, and was tasked with developing the charity's communications strategy, principally to ensure public debate on controversial areas of medical research is 'informed and not irrational'.
A Trust statement said that it was Evans' own decision to leave the charity after the role was redefined.
The Wellcome Trust was founded by Sir Henry Wellcome in 1936. It donates around £600m to support research each year.