Arlene Foster will become Northern Ireland's First Minister in January 2016.
She was backed to become the leader of the DUP by the party's MPs and Assembly members.
Speaking on BBC Radio 4's Today programme, Arlene Foster said that civil partnerships are the way that same-sex relationships are recognised in Northern Ireland.
The Stormont Assembly has voted on the issue five times since 2012 and has rejected same-sex marriage in the country.
According to The Christian Institute the new DUP leader claimed that "the style may change but the fundamentals of the DUP remain the same and that's certainly one of the issues that we are very clear about."
She continued: "we very firmly believe that marriage is an institution between a man and a woman and that should remain the same."
Arlene Foster has represented Fermanagh and South Tyrone for more than a decade, and she will lead the largest party in the Northern Ireland Assembly, with 38 MLAs.
A legal challenge to Northern Ireland's ban on gay marriage opened in early December, launched by two couples who were granted permission to judicially review the Stormont Assembly's repeated refusal to legislate for same sex marriage.
Northern Ireland is the only part of the UK or Ireland where civil marriage is denied to gay couples, following the Republic of Ireland's 'yes' vote in a referendum in May.
The majority of MLAs voted in favour of introducing gay marriage however despite this the proposal fell because unionists who oppose the move deployed a controversial voting mechanism to effectively veto the decision.
In early 2015, around 20,000 campaigners staged a march through Belfast city centre demanding a change in the law.
