A total of 314 MPs voted in favour on Friday, with 291 against the bill, clearing its biggest parliamentary hurdle.
The "Terminally Ill Adults (End of Life)" law would give mentally competent, terminally ill adults in England and Wales with six months or less left to live the right to choose to end their lives with medical help.
The vote puts Britain on course to follow Australia, Canada and other countries, as well as some US states, in permitting assisted dying.
Supporters say it will provide dignity and compassion to people suffering, but opponents worry that vulnerable people could be coerced into ending their lives.
The bill now proceeds to Britain's upper chamber, the House of Lords, where it will undergo months of scrutiny. While there could be further amendments, the unelected Lords will be reluctant to block legislation that has been passed by elected members of the House of Commons.
Prime Minister Keir Starmer's Labour government was neutral on the legislation, meaning politicians voted according to their conscience rather than along party lines. Starmer had previously said he was in favour of allowing assisted dying.
Opinion polls show that a majority of Britons back assisted dying.
Friday's vote followed hours of emotional debate and references to personal stories in the chamber and followed a vote in November that approved the legislation in principle.
The vote took place 10 years after parliament last voted against allowing assisted dying.
Opponents of the bill had argued that ill people may feel they should end their lives for fear of being a burden to their families and society, and some MPs withdrew their support after the initial vote last year, saying safeguards had been weakened.
The 314 to 291 vote for the bill compared to the last November's result, which was 330 to 275 in favour.
In the original plan, an assisted death would have required court approval. That has been replaced by a requirement for a judgement by a panel including a social worker, a senior legal figure and a psychiatrist, which is seen by some as a watering down.
The Labour MP who proposed the bill, Kim Leadbeater, said that the legislation still offered some of the most robust protections in the world against the coercion of vulnerable people.
Hundreds of campaigners both in favour and against the legislation gathered outside parliament on Friday to watch the vote on their mobile phones.
Those in favour chanted "my decision, my choice", holding up posters that said "my life, my death" and photos of relatives who they said had died in pain.
Those against the legislation held up placards that said "let's care not kill" and "kill the bill not the ill".
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