The new team of specialists will join the Department for Transport and tackle delays to road and rail schemes.
It will be led by Darren Shirley who is currently Chief Executive of the green lobbying group Campaign for Better Transport.
Before that he worked for Which? Magazine, Greenpeace and the wildlife charity WWF.
The Acceleration Unit will “engage experts with significant experience in delivering infrastructure projects”.
These will include Highways England’s Director of Complex Infrastructure projects, Chris Taylor, who oversaw the construction of the £1.5 billion A14 scheme and Mark Reynolds Chief Executive of Mace.
Shapps said: “The creation of our new Acceleration Unit and investment in our roads and railways will ensure we build back better, greener and faster in the future.”
Shirley added: “I am delighted to take on this important new role, bringing a fresh perspective and external advice to accelerate the delivery of key infrastructure projects and programmes.
“The breadth and depth of expertise in my new team will stand us in a good stead as we look to deliver the schemes that will help the country to rebuild faster through decarbonising the transport system and levelling up Britain as we emerge from the Coronavirus crisis.”