Ministers said the move, announced at the Conservative Party conference in Birmingham, was an "important step forward for equality".
It follows a Supreme Court ruling that legislation on civil partnerships, which are currently open only to same-sex couples, was in breach of the European Convention on Human Rights.
Rebecca Steinfeld and Charles Keidan (pictured above), a couple from London had taken their case to the Supreme Court.
The Government said extending them to opposite-sex couples in England and Wales would provide greater security for those who wanted legal recognition for their relationship but did not want to get married.
In a statement Mrs May said: "This change in the law helps protect the interests of opposite-sex couples who want to commit, want to formalise their relationship but don't necessarily want to get married.
"As home secretary, I was proud to sponsor the legislation that created equal marriage.
"Now, by extending civil partnerships, we are making sure that all couples, be they same-sex or opposite-sex, are given the same choices in life."
Christian charity CARE has criticised the move.
In a statement, spokesperson James Mildred said: "Coming off the back of the Government's rush to implement no fault divorce, coupled with today's announcement it's a double whammy.
"There is a real narrative developing that this is a Government unwilling to back marriage.
"We recognise that for some civil partnerships reflect a genuine desire to commit. We think though that marriage is the gold standard of commitment.
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