MPs in the lower House of Commons voted 367 to 113 in favour of the measures, which will become law if approved by the upper House of Lords on Monday.
"Today's vote is an important step towards being the first country in Europe to make standardised packaging regulations," said Public Health Minister Jane Ellison.
"Subject to the vote in the House of Lords, we expect the regulations to come into force in May 2016, bringing one step closer the prospect of our first smoke-free generation," she added.
Darker colours such as olive green are proposed, as they are believed to represent danger.
The tobacco industry and pro-tobacco campaigners insisted that the law was a sign of government overreach, with the Tobacco Manufacturer's Association saying there was a "complete lack of evidence that the policy will work".
Simon Clark, of the smokers lobby group Forest, added: "Consumers are fed up being patronised by politicians of all parties. Smokers know there are health risks associated with tobacco. Plain packaging won't make any difference.
The regulations would follow a similar step by Australia, which introduced plain packaging for cigarettes in 2012.
Smoking rates have fallen in Australia since the introduction of plain packaging, but tobacco companies argue that tax hikes are responsible for the decline.
Prime Minister David Cameron voted in favour of the change, according to his official spokesman, but many in his Conservative Party did not.