Mr Wright is currently project development director at Network Rail and before that was director of infrastructure and utilities at the Olympic Delivery Authority. He joins Crossrail in the summer, taking over from Andy Mitchell, who left earlier this year to become chief executive of Thames Tideway Tunnel.
Crossrail chief executive Andrew Wolstenholme said: "Simon Wright is an outstanding candidate who successfully led the delivery and commissioning of the infrastructure for the London Olympic and Paralympic Games; Crossrail will benefit enormously from his knowledge and expertise.
"The Crossrail programme is now over halfway to completion with the end of major civils in sight and a team fully engaged on delivering stations fit-out and the transition to an operational railway. Simon will lead the delivery team during this important second half as we move closer to realising this critically important project for London and the UK."