The 8-road depot will be able to accommodate 33 trains while routine maintenance is carried out.
Around 250 construction jobs will be created at the site.
Project Manager James Mendis said: “The award of this important contract is the latest stage of Taylor Woodrow’s extensive involvement with Crossrail.
“Our role at Old Oak Common will allow us to demonstrate our extensive capabilities in delivering railway infrastructure projects. “
Bombardier landed the Crossrail contract earlier this year covering the supply, delivery and maintenance of 65 new 200m-long trains.
Bombardier will manufacture and assemble the trains at their Derby plant, with the first due date to be delivered in May 2017.
The new fleet will be progressively introduced to the existing rail network, well in advance of services commencing through Crossrail’s central section in December 2018.