Abellio UK managing director Dominic Booth will step in temporarily after Mr Verster announced in January he was leaving following poor train performance by the ScotRail Alliance with Network Rail.
Mr Booth will remain in charge for three months until Alex Hynes, Mr Verster’s permanent replacement, takes over in June.
Mr Hynes is managing director of the Northern rail franchise, which runs trains across the north of England.
Mr Verster has denied his departure was linked to poor punctuality, but it is understood that Abellio was impatient for a change of leadership.
A ScotRail Alliance spokesman said: “Alex has a proven track record of delivering rail improvement programmes and focusing on the needs of customers.
“We are delighted he will be joining the ScotRail Alliance on 1 June.
“In the interim, Abellio managing director Dominic Booth will be taking overall responsibility for running the ScotRail Alliance.”
Mr Verster, who joined the alliance in 2015, is to lead the construction of an Oxford-Cambridge line.