The move will end the current situation where responsibility for tackling flooding is spread between government, local authorities and other organisations.
This has led to confusion about who is responsible for specific matters relating to rain induced floods.
"The Agency will be given the strategic overview for all flooding issues," said Woolas, speaking at the NCE's 'Future of UK Water Resources' conference.
"Local authorities will take responsibility for surface water flooding in their communities. It seems to me that they are best placed to deal with this issue," he said.
The Agency is already responsible for river and coastal floods.
Woolas' announcement pre-empts Sir Michael Pitt's 'lessons learned' review into the floods of 2007, which will be published next week. The government has also set-aside £34.5M to carry out any work Pitt's report will propose.
Pitt had previously claimed his final report would recommend that local authorities would need dedicated flood engineers (NCE 24 January). However, the Government’s proposals revealed by Woolas are designed to remove this highly costly requirement by giving local authorities pooled Agency resources.
Woolas said he hoped local authorities would not ask for more money to drive through schemes to deal with potential surface water floods, but a senior government source told NCE that this would be, "highly likely".
The proposals will form part of the draft Floods and Water Bill, to be announced in December's Queen's speech. The bill will enable the Agency to order landowners to carry out flood prevention work. If landowners refused, Woolas said that the Agency could be given "the power under statute to carry out the work themselves, then charge the landowner for the work they’ve done."
University of Sheffield professor of urban drainage Richard Ashley said the success of the shake up will depend on "who will replace Barbara Young as chief executive of the Agency," and whether that person has technical experience.
"The Agency has to deal with its two functions – its environmental function and its function to look after people," said Ashley.
"But in principle this could work."
Woolas added that the new legislation would also change the current situation where water regulator Ofwat prevents the construction of upstream measures which would protect downstream water infrastructure.
The need to build such preventative measures was highlighted by the plight of Mythe treatment works near Tewkesbury, Gloucestershire flooded last summer, leaving 140,000 people without mains drinking water.