Speaking today, Cameron said improving connectivity and reducing journey times between northern cities was a "crucial part of our long term economic plan for the north to boost businesses and create more jobs and security for hardworking people".
He said a new body called Transport for the North will be created, which will work with the government to provide a transport strategy for the region, including options, costs and a delivery timetable for a "HS3" east-west rail connection.
It is due to provide an interim report in March.
The government said the creation of Transport for the North, which will be made up of the main northern city regions, would "allow the north to speak with one voice on the big decisions to benefit the region as a whole".
The Prime Minister’s comments were made in response to a report by High Speed Two (HS2) chairman Sir David Higgins, which outlined the importance of improving east-west connectivity across the North.
The report said a high-speed link could cut journey times between Leeds and Manchester from around 55 minutes to between 26 and 34 minutes.
Transport secretary Patrick McLoughlin said: "Our northern cities are on the brink of an economic transformation and today’s report underlines how we can secure this by bringing those cities together to maximise the benefits of good transport links.
"HS2 is crucial to this, and I welcome Sir David’s findings on how we can ensure the phase two route delivers maximum economic benefits throughout the midlands and the north. But as he says, it is only through linking the east and west of the region that we can really unlock these benefits, not just along the route itself but right across the north."
Jeremy Hinds, planning director at consultancy Savills and head of the HS3 Working Group at the firm, said the proposals for HS3 had "the potential to be a game changer for the North".
He said: "Investment in infrastructure on this scale, and improving connections to the rest of the UK, are key ingredients to realising the unlocked potential in the North. It should transform the way we think about ourselves both economically and geographically and in business terms it is extremely welcome.
"The sooner we have a clear commitment, in terms of timing and delivery, from the government, backed by political consensus across the three main parties, the better."