If the move is cleared by House of Lords as well, every cigarette packet will have the same generic look except for the make and brand name from May 2016.
Under the new law, the packaging of all cigarettes sold in England will have to uniform in size, shape and design, with only the brand name and graphic health-warning images permitted on the front.
A dark colour such as olive green is favoured for the packaging.
Some 367 MPs voted in favour of standardised packaging, with 113 against it.
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Number 10 Downing Street confirmed that David Cameron, the Prime Minister, voted in favour of the ban.
His official spokesman said: "He has pleased it has gone through."
The chief executive of Cancer Research UK, Harpal Kumar, described the vote as historic.
He said: "During the last three years we've seen the evidence grow about the impact of tobacco packaging. Strong support for removing the slick marketing of today's packs has increased among the public and across the political spectrum.
Imperial Tobacco has said it would sue the UK government to protect its intellectual property rights.
The Australian government is defending its introduction of plain packaging in a case before the World Trade Organisation (WTO).