Iain Lobban, who heads up GCHQ, the Government's listening centre, said that the "UK's continued economic wellbeing" is under serious threat from the attacks.
Writing in The Times, Lobban confirmed that sensitive data on government computers has been targeted by hackers and criminals, along with the IT infrastructure of defence, technology and engineering firms.
He added that the Foreign Office was hit by a "significant" internet-based hacking attempt in the summer, but that ultimately proved unsuccessful.
The warning from Lobban was published ahead of a conference in London on cyber-security, in which political leaders and technology experts will come together to tackle the growing threat.
Convened by foreign secretary William Hague, the meeting is expected to be attended by US Secretary of State Hillary Clinton, EU digital chief Neelie Kroes, Wikipedia founder Jimmy Wales and Cisco vice-president Brad Boston.
There have been various high-profile hacking attempts this year, with Sony Pictures, News International, Nintendo and the Serious Organised Crime Agency all being targeted.
In April, Sony was forced to take down the PlayStation Network after a hacking attack put the personal information and credit card details of millions of members at risk of theft.
> PlayStation Network revenue up 14% after global outage, reveals Sony
Lobban agrees with Hague that a "global co-ordinated response" is required to tackle the issue of cyber crime and terrorism.
"The volume of e-crime and attacks on government and industry systems continues to be disturbing," he wrote.
"I can attest to attempts to steal British ideas and designs - in the IT, technology, defence, engineering and energy sectors, as well as other industries - to gain commercial advantage or to profit from secret knowledge of contractual arrangements.
"Such intellectual property theft doesn't just cost the companies concerned; it represents an attack on the UK's continued economic wellbeing."
Lobban warned that the government's online taxation and benefits services could be hit by cyber attacks in future, while a "black economy" was forming involving the credit card details of UK citizens being offered for sale.
"We are witnessing the development of a global criminal marketplace - a parallel black economy where cyber dollars are traded in exchanged for UK citizens' credit card details," he said.
The Ministry of Defence said that it has stopped more than 1,000 cyber attacks in the last year from criminals and overseas intelligence services.
Ministers claim that cyber security is now among their top priorities, with £650m of additional funding announced last year to tackle computer-based threats.
Graham Cluley, from IT security firm Sophos, told Sky News Online that the internet is fast becoming the new frontline of global defence strategies.
"Those countries already working together on security, like Nato, will be discussing how to protect themselves on the internet as well," he said.
"Sensible steps are what's needed. Let's not panic, but make sure you have all of your pieces in order so you can protect your firm."