The first exercise, a staged attack on the financial sector, will take place later this year, Downing Street said.
The "unprecedented" arrangement between the two countries was announced as Prime Minister David Cameron held talks with US President Barack Obama.
Agents will also co-operate in "cyber cells" on both sides of the Atlantic.
Downing Street said the cells, involving MI5 and the FBI, were the first the UK had established with another country.
They will aim to improve the flow of information between the US and UK about threats.
The measures come in the wake of the recent hacking of Sony Pictures' computers and the US military's Central Command's Twitter feed, where comments were posted promoting Islamic State (IS) militants.'Growing danger'
Speaking to BBC political editor Nick Robinson after arriving in Washington on Thursday night for a two-day visit, Mr Cameron said cyber attacks were "one of the big modern threats that we face".
The first war game will involve the Bank of England and commercial banks, targeting the City of London and Wall Street, and will be followed by "further exercises to test critical national infrastructure", Downing Street said.
Money will also be made available to train "the next generation" of cyber agents.
Mr Obama has said cyber threats were an "urgent and growing danger" and unveiled domestic proposals to strengthen the law.
The US Centcom Twitter account was suspended on Monday following an attack by hackers claiming to support Islamic State.
Prior to this the cyber attack on Sony Pictures Entertainment led to data being leaked from its computers exposing emails and personal details about staff and stars.
The hackers, who called themselves #GOP or Guardians of Peace, also threatened cinema chains planning to screen Sony's satirical North Korea comedy, The Interview, the plot of which involves a bid to assassinate the country's leader Kim Jong-un.
Sony initially cancelled the film's release after leading US cinema groups said they would not screen it, a move which Mr Obama later described as "a mistake".'People's prosperity'
The UK's National Audit Office warned in 2013 that a lack of skilled workers was hampering the fight against cyber crime.
Mr Cameron said the UK was already prepared for a cyber attack, saying GCHQ had "massive expertise", but added more needed to be done.
"This is a real signal it's time to step up the efforts and to do more," he said.
"It's also about protecting people's data, people's finances - these attacks can have real consequences to people's prosperity."Mr Cameron's trip to Washington is expected to be his last before the UK general election
Earlier this week, Mr Cameron said in relation to cyber attacks that there should be no "means of communication" which "we cannot read".
The prime minister is expected to talk to the US president about getting companies such as Google and Facebook to allow governments to see encrypted messages.
But the BBC's technology correspondent Rory Cellan-Jones said there had been a lot of concern over Mr Cameron's words. He said not only were civil rights groups worried, but major players in the technology industry said banning encrypted messages could harm British trade if UK companies were seen to be not private.
Our correspondent also told BBC Radio 4's Today programme that smaller social networking sites were just as well used by potential hackers as the well-known ones.
He said he had found an example of an exchange on the site Ask.fm which appeared to be from an IS fighter asking another user which country he should go to for weapons training.
In relation to the site being used for this type of communication Doug Leeds, the chief executive of Ask.com, which owns Ask.fm, said: "We have taken some action, and we're looking to take more, what we have done so far is beef up our filters to try and look for patterns that would suggest that this is going on."
Mr Cameron and Mr Obama will also focus on the global economy during the prime minister's visit, which is likely to be his final Washington trip before May's general election.
The pair also discussed the fight against Ebola over dinner at the White House on Thursday, and the prime minister said epidemiologists should be deployed around the world to provide a swift response to outbreaks.