The National Hi-Tech Crime Unit (NHCTU) will be responsible for tracking down the growing range of criminals who operate in cyberspace.
They include organised criminal gangs who use computers to commit fraud, paedophiles who exchange obscene images on the net, and hackers who wreak havoc by writing computer viruses which can disable systems worldwide.
Netting criminals
Mr Straw told BBC News: "Cybercrime can affect us in all sorts of ways - obviously through financial fraud, through people using the internet and access to major databases to fiddle credit cards, but it can also be used in an even more pernicious way in respect of paedophilia.
"I've seen some of the exhibits - if you can call them that - that are available on the internet, that are run by paedophiles.
"They really are absolutely appalling."
He added: "Our overall approach is that if something is criminal offline then it is also criminal online.
"But we have to ensure that police investigatory techniques keep up with changes in technology."
As the unit expands, every constabulary in the UK is expected to be given at least one "cyber cop" to tackle internet crime in its area.
The £25m unit will draw its staff from individual police forces, Customs, the National Crime Squad (NCS) and the National Criminal Intelligence Service (NCIS).
NCS director general Bill Hughes said: "We have clearly started to see a change in the way that criminals conduct their activities.
"They look for the highest return with the least risk, and in an age where society and business are reaping the rewards and benefits of new technology, there is a massive opportunity for organised crime to exploit those new technologies.
"Looking to the future the equation is simple - money is going electronic and where money goes so will organised crime.
"As we have learnt from our colleagues in the USA, the only way to tackle this type of crime is by using a joined-up approach."
The squad is expected to deploy undercover officers in internet chat rooms in an effort to trap paedophiles.
But civil liberties groups are worried about the extent of the unit's powers.
They believe the police will also be able to intercept private e-mails of innocent people without proper authority.
Rising crime
But the unit's Detective Chief Superintendent Len Hynds told BBC News: "We have no inclination, nor the desire, nor the ability to trawl people's e-mails.
"We will be targeting those people who use the internet to commit fraud, paedophilia and other offences."
Shadow home secretary Ann Widdecombe said the new unit must be backed up by real government action.
"It is all very well for Jack Straw to talk tough, but he has repeatedly refused to act on Conservative proposals to tackle predatory paedophiles who prey on children in internet chatrooms," she said.
Miss Widdecombe hoped the unit would catch "some of the most dangerous criminals in our society".
More than 60% of Britain's online businesses have been the victims of hacking, according to estimates.
Other internet crimes are aimed at causing maximum disruption.
Last May a computer virus called the Love Bug was released by a lone computer user in the Philippines.
The virus spread by e-mail to affect hundreds of thousands of businesses and personal computers across the world. The US Government was among those hit.