Mr Obama pointed out that al-Qaeda and other groups had threatened computer warfare.
Acts of terror today, he said, could come "not only from a few extremists in suicide vests, but from a few key strokes of a computer - a weapon of mass disruption."
The president said the United States was particularly dependent on its computer networks and therefore particularly vulnerable to cyber attacks.
In 2007 alone the Pentagon reported nearly 44,000 incidents of what it called malicious cyber activity carried out by foreign militaries, intelligence agencies and individual hackers.
Mr Obama said that protecting America's digital infrastructure, the networks and computers everyone depended on every day, would be "a national security priority".
"It is now clear," he said, "this cyber threat is one of the most serious economic and national security challenges we face as a nation."
He said the United States had failed to invest in its digital infrastructure. "We are not as prepared as we should be," he said.
In the past, no one US department was responsible for cyber-security, resulting in poor communication and co-ordination, he said.
The new cyber-security office will be a multi-billion dollar effort designed to restrict access to government computers and to protect systems - such as those that run the stock exchange and air traffic control - that keep the country going.
HACKING THE US
April 2009: US government admits power grid is vulnerable after media reports that Chinese and Russian spies have planted software that could shut it down
April 2009: China denies hacking into a system containing data on a new US fighter jet
Nov 2008: Congressional panel says China has stepped up computer-based espionage and is stealing "vast amounts" of sensitive information
Sep 2007: China denies reports its military hacked into the Pentagon in June of that year
But Mr Obama emphasised that it would also help protect individual Americans, adding: "Millions... have been victimised: their privacy violated, their identities stolen, their lives upended, and their wallets emptied."
He pointed out that according to one survey, cyber crime cost Americans more than $8bn over the last two years. Worldwide, it was estimated that cyber criminals stole intellectual property from businesses worth up to $1 trillion.
"In short, America's economic prosperity in the 21st century will depend on cyber-security," he said.
The Obama administration is also expected to create a new cyber command at the Pentagon with the dual task of eradicating potential vulnerabilities in America's sensitive computer networks, while simultaneously creating ways to exploit them in the systems of potential enemies.
An influential study published last year suggested that having an offensive computer warfare capability would have a deterrent effect against would-be attackers.
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