The money will fund flood defences in Yorkshire, a £10m innovation fund for businesses in Manchester and Cheshire, and regeneration in Hull city centre.
It was announced by Prime Minister Theresa May amid plans for a new more interventionist industrial strategy.
Mrs May said there was a need to "drive growth across the whole UK".
She detailed the funding during her first regional cabinet meeting, held at a science and business park in Daresbury, Cheshire.
The money will help fund projects including:
What is the Northern Powerhouse?
The £556m has been allocated from the Local Growth Fund cash pot of £1.8bn, announced in the Autumn Statement, and will be handed to 11 Local Enterprise Partnerships across the north.
It is part of a wider scheme aimed at boosting the post-Brexit UK economy and creating jobs, with a particular focus on investment in science, research and innovation.
Mrs May said the plans, contained in a green paper published earlier, were about building a "truly global Britain".
While a significant portion of money has been allocated to the North, she said there was "the need to ensure that our economy works for everyone in every part of the country".
News of the funding earmarked for flood defences has been particularly welcomed, following the widespread deluge that hit parts of Yorkshire and Lancashire in December 2015.
Councillor Alex Ross-Shaw, Bradford City's Council executive member for regeneration, said: "We need to examine the detail but I welcome much-needed investment to help protect homes and businesses in our district from future flooding.
"The Boxing Day floods a year ago had a devastating impact on those affected and the region's economy, so it's essential that the government works with us to manage flood risk because this is about people's homes and livelihoods."
Stacey Howard, operations director at the Goole Development Trust, said improved transport links would be "brilliant for the town".
"We are in the M62 corridor and Goole is the biggest inland port in the UK."
Mike Perls, founder and CEO of Manchester-based strategic marketing agency MC2, said the funding "isn't about about factories and chimneys", but rather "a modern industrial strategy" to help modern, innovative businesses thrive.
"It will encourage regional economies to develop strategies reflecting their strengths, and the businesses within to look globally without hesitation."
However, Rebecca Long-Bailey MP, Labour's Shadow Chief Secretary to the Treasury, said £556m "pales into insignificance" when set against recent central government cuts to local councils.
"Local authorities lost £18bn of government funding in real terms between 2010 and 15, with the poorest councils bearing the brunt of the cuts.
"From what we have seen of the government's industrial strategy so far, I am not convinced they are committed to the long-term investment needed to transform the northern economy."
Business Secretary Greg Clark said the plans were about "spreading opportunities right across the country".
But his opposite number at Labour, Clive Lewis, said the government's industrial strategy was "too little too late".

Mark Munro, 31, and James Robertson, 27, pushed Russell Robertson over railings at Bainsford Bridge, Falkirk, on 29 May last year.
Mr Robertson, 27, suffered a skull fracture caused by his head hitting a metal stanchion as he fell.
The two men, who were accused of murder, were convicted of the lesser charge of culpable homicide.
The High Court in Glasgow heard that Mr Robertson would have been unconscious when he went into the water.
His body was recovered from the canal more than an hour later.
The court heard that all three men had been at the Warehouse nightclub in Falkirk and were making their way home after 03:00 when an incident occurred.
James Robertson was approached by Russell Robertson and they began fighting, before Munro, who had been on the phone, became involved.
The trial heard the men tipped Mr Robertson into the canal and then ran off without a backward glance.
Both accused blamed each other during the trial.
Robertson admitted being in an initial struggle with Russell Robertson, but claimed he was walking away towards Falkirk when he went into the water.
Nightclub security manager Kevin Gibney said he saw Russell Robertson disappear off the bridge as he struggled with Munro and Robertson.
Mr Gibney said: "One minute he was there and the next he was gone. The two gentlemen ran across the road."
Judge Lady Carmichael deferred sentence until 23 August at the High Court in Edinburgh and detained both men in custody.
Business leaders and politicians have welcomed a newly-allocated cash injection of £556m for the government's Northern Powerhouse project.
[NEXT_CONCEPT]
Two men have been convicted of killing a stranger by throwing him over a bridge into a canal.