He was "fine" with same sex marriage, he said in an interview after his election, despite previously saying "marriage should be between a man and a woman".
Many conservative and evangelical Christians had expected Trump to take steps to overturn the ruling on same sex unions.
It was legalised in all American states after a Supreme Court ruling in 2014. During his election campaign Trump promised to appoint judges to the court who would vote in a conservative way.
In 2011, whilst considering running for the White House, Trump told Fox News "I just don't feel good" about same sex marriage.
But in his first interview since being elected Trump told CBS "it's done".
"These cases have gone to the Supreme Court. They've been settled. And I'm-I'm fine with that" he said.
The president-elect did, however, confirm his commitment to prolife issues.
He confirmed he would appoint prolife judges to the Supreme Court that could overturn a ruling that made abortion legal in all states.
The issue could be left to individual states to decide upon, he suggested.
"It's got a long way to go, just so you understand. That has a long, long way to go," he stressed.
Trump is widely considered to have won the White House thanks to overwhelming support from evangelical Christians.
More Christians in every denomination voted for the businessman that his Democrat rival Hillary Clinton, who supported abortion and gay marriage.