Gay couples may already have civil partnerships but campaigners say the distinction gives the impression that society considers gay relationships inferior.
Mr Cameron has stressed he is a strong backer of gay marriage but does not plan to force his party's members of parliament to vote in favour of legislation, which will apply to England and Wales and be introduced by the end of the current parliament in 2015.
Scotland has separate plans for same-sex marriage.
Opponents of the measure include the Church of England and several members of Cameron's own party.
"In each century parliament has acted, sometimes radically, to ensure marriage reflects our society, to keep it relevant and meaningful," culture secretary Maria Miller told parliament.
"For me, extending marriage to same-sex couples will strengthen, not weaken, this vital institution, and the response I'm publishing today makes clear that we will enable same-sex couples to get married through a civil ceremony," she said.
"We will also enable those religious organisations who wish to conduct same sex marriages to be able to do so," she added.
However, she made clear that under the proposals it would remain illegal for churches belonging to the Church of England to marry gay couples - an exclusion the established church itself requested.
Other religious groups, such as Quakers and liberal Jewish groups, could choose to marry gay people, but under the proposals no individual minister would be compelled to marry a same-sex couple.
Gay rights group Stonewall welcomed the legislation.
"We're delighted about the government's statement today and welcome the promise to legislate for equal marriage as warmly as on the three previous occasions that this announcement has been made," said Stonewall Chief Executive Ben Summerskill.
"While we fully respect the point of view of those who oppose the government's plans, our advice to them remains that if you don't approve of same-sex marriage, then just make sure you don't get married to someone of the same sex," he added.
The move to legalise gay marriage comes after a public consultation on the issue, and is seen by political analysts as a way for Mr Cameron to broaden the appeal of his centre-right Conservative Party and burnish its liberal values.
Same-sex marriage is backed by many prominent Conservatives and the party's partners in coalition government, the Liberal Democrats, as well as the opposition Labour Party.
However, the plan has run into strong opposition from some Conservative MPs on religious grounds and because of what they say is a lack of a democratic mandate.
Opinion polls on the issue have shown mixed results.
Eleven other countries have already legalised same-sex marriage.
The US Supreme Court stepped into the debate for the first time last week by agreeing to review two challenges to federal and state laws that define marriage as a union between a man and a woman.