Miller said the couples have another deadline if they want to be among the first to tie the knot. They must declare their intention by March 13.
"Marriage is one of our most important institutions, and from March 29, 2014, it will be open to everyone, irrespective of whether they fall in love with someone of the same sex or opposite sex," Miller said.
"This is just another step in the evolution of marriage and I know that many couples up and down the country will be hugely excited that they can now plan for their big day and demonstrate their love and commitment to each other by getting married."
The government pushed up the time by a few months. Many people had assumed same-sex marriage, recently approved by Parliament, would not become legal until July.
Miller said March is also an important month for same-sex couples who married legally elsewhere and are now considered civil partners in Britain. They will become legal spouses in March.
Couples who want to marry under British law overseas, at consulates or at chapels on military bases, will have to wait until June.
Ben Summerskill, head of the advocacy group Stonewall, said he was "delighted" with the announcement and especially pleased because Miller made it on United Nations Human Rights Day. He also advised same-sex couples planning their weddings that no one has a right to refuse their business because of their orientation.