Newly headhunted as a CLRL non-executive director, Dwyer was one of the contractors who served as chairman of the British side of the TransManche Link consortium that built the Channel Tunnel in the 1980s and 1990s.
On the project, Dwyer was in constant negotiations with famously abrasive Eurotunnel chairman Sir Alistair Morton, himself under pressure from the project's bankers.
"The funding mechanism [for Crossrail] is quite complex and I think they needed someone with experience of dealing with the financial world as chairman of a public company but at the same time understanding the engineering issues," said Dwyer.
He predicted that tying all the funding streams together would be one of the biggest challenges on the project.
"I've been assured that the funding is in place but finance is going to be the challenge.
"Internationally we are going through a difficult time in terms of the liquidity of the banking system."
The government's spending plans would be tighter and further pressure could be added if other projects in London, like the 2012 Olympics, cost more than expected, he added.
Dwyer joins Crossrail after nine years as chairman of the regeneration company Liverpool Vision.
"The offer coincided with me stepping down from Liverpool Vision. A new company is being created to replace it which I didn’t want to be a part of."
Dwyer will work closely with executive chairman Doug Oakervee who was an ICE vice president during Dwyer's presidential year from 2000 to 2001.
Other appointed non executive directors for CLRL include chairman for the Museum of London Michael Cassidy; chief executive of the Export Credits Guarantee Department Patrick Crawford and executive deputy chair of Millwall FC Heather Rabbatts.