EU Trade Commissioner Pascal Lamy welcomed the US climbdown and vowed the transatlantic trade feud would end, at least over the steel issue.
"These sanctions as I've always said were there as a tool for compliance. They've complied, and the sanctions will disappear," Lamy told a news conference after the White House announcement.
Lamy also said that the Commission - the EU's executive arm - would remove safeguard measures imposed to ward off a flood of steel imports diverted by other countries to the EU because of the US tariffs.
The EU had threatened to impose $2.2 billion (1.82 billion euros) of sanctions on imports of US textiles, shoes, fruit and vegetables - targeted against electorally important states - if Washington failed to lift its tariffs by 15 December.
But the White House averted a trade war by announcing the tariffs had "now achieved their purpose and, as a result of changed economic circumstances, it is time to lift them".
"This is obviously good news: good news for European steel makers, good news for European steel workers, good news for Europe," Lamy said.
"I'm glad this is the end of this story, which would have cost us quite a bit of trade," he said, while warning that the EU would continue action at the World Trade Organisation on other contentious US trade measures.
Britain's government and business leaders also welcomed Bush's decision. The UK's Trade and Industry Secretary Patricia Hewitt said she was "delighted" by the announcement.
"Our steel industry will be hugely relieved," Hewitt said.
She said the tariffs had cost British firms thousands of tonnes of lost exports and had damaged the country's steel industry.
Britain had backed the rest of the European Union in calling on the United States to scrap the tariffs.
British industry leaders and Prime Minister Tony Blair urged Bush during his state visit last month to heed a ruling by the World Trade Organisation that the tariffs were illegal.
Blair (R) pressed Bush to listen to calls for an end to the tariffs
The director general of the Confederation of British Industry, Digby Jones, said businesses on both sides of the Atlantic would welcome the news that the US administration had "come to its senses".
He said, "US steel producers may have seen some short term benefit but US steel users paid the price, in jobs and loss of competitiveness.
"It would have been absurd to inflict even more unnecessary damage on America and Europe by forcing justifiable EU retaliatory action. Everyone loses when politicians engage in trade wars."