Former HS2 Ltd chairman Douglas Oakervee will lead the inquiry, with Lord Berkeley - a long-term critic of the high-speed railway scheme - acting as his deputy.
The DfT said the review will consider a number of factors relating to HS2, including its benefits, impacts, affordability, efficiency, deliverability, scope and phasing.
This will "inform the Government's decisions on next steps for the project", according to the DfT.
The launch of the review comes amid growing concern that HS2 cannot be built to its current specification within the £55.7 billion budget.
Mr Shapps said: "The Prime Minister has been clear that transport infrastructure has the potential to drive economic growth, redistribute opportunity and support towns and cities across the UK, but that investments must be subject to continuous assessment of their costs and benefits.
"That's why we are undertaking this independent and rigorous review of HS2.
"Douglas Oakervee and his expert panel will consider all the evidence available, and provide the department with clear advice on the future of the project."
Mr Oakervee said: "The Prime Minister has asked me to lead this important review into the HS2 programme.
"I am looking forward to working with my deputy, Lord Berkeley, to advise the Government on how and whether to progress with HS2, based on all existing evidence."
- Reducing the speed of the trains;
- Making Old Oak Common the London terminus "at least for a period", instead of Euston;
- Building only Phase 1, between London and Birmingham;
- Combining Phase 2a - extending the line to Crewe - with Phase 1;
- Altering plans for Phase 2b, which currently involves taking the line to Manchester and Leeds.
The DfT said limited, largely preparatory work on the project will continue in parallel with the review.
Transport minister Baroness Vere told the House of Lords last month that £7.4bn had already been spent on HS2.
The figure includes money towards the purchase of land and property, ground investigation work, technical designs, IT systems, wages and public engagement.
A recent Financial Times report stated that HS2 Ltd chairman Allan Cook wrote to the DfT warning the final bill could reach as much as £85bn.
The feared price hike is believed to be due to various factors including engineering costs, poor ground conditions, under-estimating the cost to purchase land and property, and the expense of running trains at up to 225mph, which is faster than comparable projects.
Former Labour transport secretary Lord Adonis claimed the review was "about as stupid as you can get" as it "screws Birmingham and the North".
Writing on Twitter, he added: "Classic Johnson. It throws project into flux and will cause big delays, loss of confidence and cost increases. But HS2 will almost certainly continue afterwards in modified form. What a shambles."
A YouGov survey of 2,779 Britons carried out in May indicated that 40 per cent of people oppose the building of a high-speed rail line along the route planned for HS2, with 32 per cent in support.
Nearly half (49 per cent) of Conservative voters polled said they were against such a scheme.