The Prime Minister will take a swipe at Labour by claiming that dithering over the project will condemn Britain to the slow lane.
He is expected to tell the CBI's annual conference that "fortune favours the bold - not the weak and indecisive". The scheme needs cross-party approval to stand a chance of being built, but shadow chancellor Ed Balls threw Labour's support into doubt with concerns about the spiralling costs, insisting he would not sign a "blank cheque".
Mr Cameron is due to announce that Sir David Higgins' first job will be to report on lowering costs and maximising benefits.
He is expected to say: "Britain is in a global race for jobs and wealth. Our infrastructure is decades out of date and we urgently need to invest and build.
"Those who want to delay or obstruct HS2 show a lack of vision. They are playing politics with Britain's prosperity. They are betraying everyone north of Watford. And they want to condemn Britain to the slow lane."