Phase 2b of the scheme connecting London and the North will not be complete until between 2035 and 2040 - compared with the original target deadline of 2033 for the section from Crewe to Manchester and Birmingham to Leeds.
Allan Cook, the recently-appointed chairman of HS2 Ltd, said the cost of Phase 2b was likely to rise from £28.6bn to a range of £32bn to £36bn.
At the same time the Government revealed that the scheme as a whole cannot be delivered within the original budget of £55.7bn and will actually require a budget of between £72bn and £78bn in 2015 prices.
This is the equivalent to £81 to £88 billion in 2019 prices, against an original budget equivalent to £62.4 billion.
Phase One from Birmingham to London will also not be finished in line with the original deadline and will not have a staged opening between 2028 and 2031.
The news broke on the day Mr Cook spoke at the HS2 Economic Growth Conference in Leeds. Organisers said he would be "sharing his views on the importance of the project to the UK’s economic future, the benefits it is already delivering and the huge regeneration and development opportunities it will bring".
And a new campaign, Connecting Britain, was launched by political leaders to underline the importance of both HS2 and Northern Powerhouse Rail (NPR).
Reacting to the news, David Davis, MP for Haltemprice and Howden and former Brexit Secretary, wrote on Twitter: "I suspect this will not be the last time we see headlines about HS2 being further delayed and billions over budget. The recently announced review into the project must scrap this white elephant."
Shadow Transport Secretary Andy McDonald said: “This government has misled both Parliament and the public about the cost of HS2. People need to have confidence in the project, so this delay is bad news for the UK transport system as a whole and the North of England in particular."
In a report described as HS2 Chairman's Stocktake, Mr Cook said the original plans for the route "did not take sufficient account of the compound effect of building a high-speed line through a more densely populated country with more difficult topography than elsewhere – and doing so whilst complying with higher environmental standards".
He added: "Equally, the existing cost/benefit model, which was designed for smaller scale schemes, has proved inadequate in capturing the full transformational effect of HS2, particularly on changing land values.
"This transformation is already being demonstrated in Birmingham. Therefore, the budget and target schedule for the programme have proved unrealistic, while at the same time the benefits have been understated.
"Given the above, the budget, schedule and business model for HS2, as well as the way it interfaces with the rest of the rail network, need to be reset – reflecting the different maturity of the Phases – to ensure the programme delivers the greatest possible benefit for the country in the most cost-effective way."
His report said the hybrid Bill for Phase 2b running from Crewe to Manchester and Birmingham to Leeds is "currently being prepared and is, therefore, the least mature of the phases".
He said: "Given its early stage and its essential role in delivering Northern Powerhouse Rail, Transport for the North and Midlands Connect, there is an opportunity to fully integrate the plans for each region and deliver them in smaller, more manageable sections as part of a rolling programme of investment in the Midlands and the North.
"In line with the experience of Phase One, the cost of Phase 2b is likely to rise from £28.6bn to a range of £32bn to £36bn with target delivery moving from 2033 to between 2035 and 2040."
Earlier this month, a government inquiry into whether and how HS2 could proceed was launched, which included how it would fit in with the proposed Northern Powerhouse Rail project connecting the big cities of the North.
In a statement issued today, Transport Secretary Grant Shapps said: "One important aspect of the panel’s work is to consider whether both the costs, and the benefits, of the scheme have been correctly identified.
"HS2’s business case has been founded on increasing capacity on our constrained rail network, improving connectivity, and stimulating economic growth and regeneration.
"The current budget was established in 2013 and later adjusted to 2015 prices. Since that time, significant concerns have been raised.
"I want the House to have the full picture. There is no future in obscuring the true costs of a large infrastructure project – as well as the potential benefits."