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 in Washington, 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 Centcom Twitter account was suspended on Monday following an attack by hackers claiming to support Islamic State.
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 that more needed to be done.
Ebola fight
"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."
The two leaders will also focus on the global economy during Mr Cameron`s two-day visit, which is likely to be his final Washington visit before May`s general election.
They also discussed the fight against Ebola over dinner at the White House on Thursday.
The prime minister is using his visit to call for a new "international rapid response team" of disease specialists.
Mr Cameron said the epidemiologists should be deployed around the world to provide a swift response to outbreaks.
He also called for an international mechanism to produce and distribute drugs and treatments for newly emerging diseases.
Downing Street said "pharmaceutical regulators and global bureaucracy" made the current process "abhorrently expensive and time-consuming".
