The future of that section of the high-speed rail line, which is set to link the West Midlands to Leeds and Crewe to Manchester, was thrown into doubt in December after the National Infrastructure Commission recommended that local rail links should be given priority.
The eastern leg has not been given the go-ahead by Parliament yet, but Mr Shapps has reaffirmed the Government s commitment to complete the project and ensure the line reaches Leeds.
He added: “With the HS2 eastern leg, it was originally assumed the development would take place and bring benefits in 2040, probably 2050. We think we can bring that forward quite dramatically by building it in a smarter way.”
The Government, which expects HS2 to cost up to £98bn, is drawing up an Integrated Rail Plan that looks at how the line can be completed ahead of schedule and integrated with Northern Powerhouse Rail.
That plan, initially expected last year, will be published “soon” but no date has been set yet, Mr Shapps added.
Henri Murison, director of the Northern Powerhouse Partnership, said: “The transport secretary and minister for the Northern Powerhouse is doing exactly the right thing in promising to deliver the eastern leg right the way to Leeds, and we now need government to publicly commit to this in the Integrated Rail Plan as soon as possible.
"It’s critical to ensuring levelling up is a reality not just rhetoric."
It comes after the government set up Great British Railways, which will set most of the prices and timetables, sell tickets in England and manage rail infrastructure, but contract private companies to operate the trains.
Mr Shapps said the Government remains committed to “levelling up” the country by completing several projects designed to improve public transport, including a £317m upgrade of the Transpennine route.
The Conservative minister said the UK “can no longer afford to hold back human enterprise” and “favour one corner of the country”.
He said: "It’s not about weakening the productivity of the South East of England. This is about raising transport quality in the rest of the United Kingdom, to the levels of the South East, marking the talent, the flair and the self-belief in regions that once led the world in productivity.
“If we can do that, then we can achieve something remarkable.
“Every part of the country unleashing the restraints of outdated public infrastructure, thereby matching the South East’s productivity - that would make the UK the biggest economy in Europe by 2050.”
He added: “I know some people think demand for rail and bus travel will never fully recover. Video conferencing, they argue, is now embedded as the way we do business. But I think that will quickly be overtaken by the reality, as our economy bounces back.”
He also said the Government is “very, very keen” to work with West Yorkshire Mayor Tracy Brabin to “kickstart” a mass transit system for West Yorkshire.