Its director Jim Gamble said negotiations with police about putting mug shots of people who have absconded from supervision on a website were "well advanced".
Fake websites
CEOP, which works with international police forces, began operating at midnight and took its first credible report of alleged activity at 0800 BST.
It is affiliated to the Serious Organised Crime Agency, the UK's new FBI-style organisation, and has a budget of £5m a year.
Mr Gamble said the aim was to make the UK the safest place for children using the internet.
"If you're a paedophile grooming an actual child, and that child has visited our website they could be cutting and pasting your conversation and sending it to us," he said.
Fake websites purporting to offer images will also be set up to lure paedophiles into disclosing credit card details, so they can be traced.
Home Office minister Paul Goggins said the aim was not to stop children using the internet but said they had to be aware of the dangers.
"The message to paedophiles and sex offenders is that we are significantly increasing our capacity to track you down and to bring you to justice," he added.
British Telecom says it blocks up to 20,000 attempts each day to access child porn and in 2005, more than 6,000 paedophile websites were reported to police - almost twice as many as the year before.
Most of the content originates abroad but young people in the UK are vulnerable to determined paedophiles who try to "groom" them online.
Police officers will work alongside computer technicians and child welfare specialists at CEOP.
Mary Marsh, director of the National Society for the Prevention of Cruelty to Children, said: "This is a major step forward in tackling online child abuse and child exploitation.
"The NSPCC is pleased to be playing a significant role as a partner."
The Internet Watch Foundation, which has worked with the industry over the last 10 years to have websites hosting obscene and racist material taken down, also welcomed the "single point of expertise".
"The Internet Watch Foundation will continue its role taking reports from the public about illegal content ... and will pass intelligence about the illegal material to the new CEOP centre to be further investigated," said the IWF's Sarah Robertson.