The govt says, the move will provide greater security for unmarried couples and their families.
And it will address the “imbalance” that allows same-sex couples to enter a civil partnership or get married – a choice denied to heterosexual couples.
The current system was found in June to be in breach of European law.
The Supreme Court unanimously ruled in favour of Rebecca Steinfeld, 37, and Charles Keidan, 41, from London, who launched their own legal bid to be allowed to have a civil partnership.
The court said that the Civil Partnership Act 2004 which only applies to same-sex couples was incompatible with the European Convention on Human Rights.
The Scottish government is also carrying out a consultation on allowing mixed-sex couples to enter into civil partnerships after the ruling.
There are more than 3.3 million unmarried couples in the UK who live together with shared financial responsibilities, nearly half of them with children, the government said.
These households do not have the same legal protections as those who have a civil partnership or marriage.
Mrs May, who is in Birmingham for the Conservative Party conference, said the move would give all couples the same choices in life.
“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,” she said.
“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.”
The government said there was “a number of legal issues to consider, across pension and family law” and ministers would now consult on the technical detail.
But Equalities Minister Penny Mordaunt promised that the change in the law would happen “as swiftly as possible”.
The government says unmarried couples in a long-standing relationship often think they have the same rights as married couples.
* They are not entitled to the same tax reliefs and exemptions for spouses and civil partners
* That includes the inheritance tax exemption and the marriage income tax allowance
* Also, if someone’s partner dies, they have no automatic right to inherit their partner’s estate – so they might not be able to afford to stay in the family home
* Bereavement Support Payments do not apply to couples who live together and they do not benefit from their partner’s state pension contributions
* Many occupational pension schemes do not offer survivor benefits to such couples
* And unmarried couples do not have a guaranteed right to the ownership of each other’s property on relationship breakdown
* They might be able to then get that through the courts.>