The lower tax rates for exports for firms, including Boeing and Microsoft, were judged an illegal subsidy by the World Trade Organisation (WTO), which ruled the EU could impose $4bn in sanctions a year on US goods.
But European Trade Commissioner Pascal Lamy decided to apply gradual pressure by phasing in the measures, which will hit a wide range of goods, including textiles, jewellery and toys.
The sanctions are intended to prod the US Congress to replace the tax breaks quickly with measures in line with WTO rules.
They start at $16mn as an extra five per cent duty on selected US products in March and rise by one per cent a month to $315mn in 2004 and $666mn if they run throughout 2005.
Based on the full $4bn, the main sector to be hit would be US jewellery at an estimated $1.43bn.
"The EU's objective remains the withdrawal of the US illegal subsidy," the commission said in a statement. "The EU has opted for a response which is measured, gradual and geared towards focusing the mind of the US legislature to comply."
Officials have tried to play down the impact of the trade row, the first time since the WTO was created in 1995 that the EU has retaliated on US goods.
"This is not the beginning of a trade war. WTO disputes are all part of the system," one Washington official told reporters ahead of the 1 March deadline for the sanctions to apply.
EU firms worried
But EU firms have expressed worries over the escalation of a dispute that could lead to extra costs as the economy splutters back to life.
Lamy has said sanctions should be seen in the light of daily transatlantic trade of $1bn, and the EU has coped since 1999 with more than $100mn of imposed US sanctions a year in a fight over beef.
The dollar's weakness is likely to lessen the pain on US exporters and the administration of President George Bush has pressured Congress to change the disputed tax laws.