The controversial bill which will ratify the Lisbon Treaty has cleared its final Commons stages.
The government says a referendum is not needed on the treaty
MPs voted by 346 votes to 206 to approve the EU (Amendment) Bill, after topic-by-topic debates over six weeks.
For the Conservatives, William Hague accused ministers of "ramming through" the bill without a referendum.
But Foreign Secretary David Miliband said the treaty was good for the UK and said Conservative "scaremongering" was "dangerous and deluded".
The Bill, which will now go to the Lords, will ratify the Lisbon Treaty - which was drawn up to replace the EU constitution, after that was rejected by French and Dutch voters in 2005.
Last week the Conservatives lost a vote on their proposal to put the treaty to a referendum - something opposed by the government and Lib Dems who say the treaty does not have constitutional implications.
Opening the final day of the lengthy Commons debate, Mr Miliband told MPs: "Last week we debated how to pass the treaty into law. Today we debate whether to do so."
He said "every mainstream political party in Europe" believed it was good for the UK and good for Europe, because it reformed the EU's "foundations" and would "allow us to move on to the agenda of prosperity and development and climate change".
He said the only major opposition party in Europe resisting it was the Conservatives who were "stuck in the past and obsessed with myths about the EU".
But shadow foreign secretary Mr Hague said the treaty would give the EU "unwarranted power" over Britain's national life.
He accused the government of "ramming through" the legislation without a referendum, in "clear breach" of its election promises , without a "democratic mandate" for the treaty.
"The truth is the foreign secretary and prime minister now believe the former prime minister (Tony Blair) made a serious error when he promised a referendum and it was that error which has reduced them to arguing that something which is 90% the same is fundamentally different," he said.
He said the promising of a referendum and refusal to give one were nothing to do with constitutional practice, but "everything to do with the sharp practice of ministers focused solely on what they could or could not get away with".
He urged Lib Dem peers to stand by the party's manifesto commitment when the bill is debated in the Lords.
But Labour former health secretary Patricia Hewitt said the Conservative Party was "talking to itself, not to the British people and certainly not to our partners in the European Union".
And for the Liberal Democrats, Edward Davey said the Commons debates had shown the treaty was "sensible and modest".
He told MPs there were many "firsts" in the treaty, including member states having the right to leave the EU and national parliaments being given a mechanism for calling a halt to EU legislation.
"This is a treaty which genuine Euro-sceptics should be coming to praise - not to bury," he said.
"The fact that they don't now back these reforms that they used to call for reflects the reality that the vast majority of Euro-sceptics aren't genuinely sceptical but actually are closed minded and pre-determined in their opposition in everything European."
But Democratic Unionist Sammy Wilson warned that by passing the legislation, MPs would be doing "irreparable damage" to their image and the powers of Parliament.