The move on the eve of the Conservatives' conference in Manchester fulfils a promise in the last Tory manifesto and will go down well in the party's ranks.
The Prime Minister said it was a recognition of the commitment, stability and responsibility marriage and civil partnerships create in people and across society.
The policy, unusually, was trailed at the Liberal Democrat conference two weeks ago as part of a LibDem-Con deal, in which Nick Clegg's party achieves its desire to see all primary schoolchildren in England receive a free healthy lunch while the Tories get to see marriage recognised in the tax system.
It is thought each policy costs around £600m. Just how both will be paid for will be explained in Chancellor George Osborne's autumn statement.
In practical terms, the tax measure will be worth £200 a year in people's pockets and will begin in 2015 although people will not see any money until the end of that tax year in April 2016. There is one main restriction - it will apply to basic-rate taxpayers only.
Tory HQ stressed Mr Cameron believed marriage was an "important institution at the heart of a strong society" and the new allowance showed how the UK Government valued commitment.
The proposal will let people transfer £1000 of their personal tax allowance to their spouse or civil partner, meaning it will apply to people whose partner is a part-time worker or perhaps a stay-at-home mother.
The PM said: "I believe in marriage. Alongside the birth of my children, my wedding was the happiest day of my life. Since then, Samantha and I have been a team. Nothing I've done since - becoming a Member of Parliament, leader of my party or Prime Minister - would have been possible without her.
"There is something special about marriage; it's a declaration of commitment, responsibility and stability that helps to bind families. The values of marriage are give and take, support and sacrifice - values that we need more of in this country."
He explained that when he ran for the party leadership in 2005 he made it clear he wanted to do more for marriage in the tax system. He repeated this personal pledge in the party's 2010 election manifesto. "So this week at the Conservative Party's conference in Manchester, I'm going to deliver on the promise I made."
He stressed the allowance would be available "if you're gay or straight and in a civil partnership or a marriage" and added: "This summer I was proud to make Equal Marriage the law. Love is love, commitment is commitment."