It has also said it hopes people will "stay calm" and "hold on" after the decision and give it time to see how it will pan out.
The Kirk voted through the change at its General Assembly in Edinburgh yesterday with 339 voting in favour and 215 voting against.
It means congregations who want to can take ministers already in same-sex marriages and that ministers can get married to someone of the same-sex if they wish.
The vote does not permit same-sex marriages within the Church of Scotland.
It follows a vote last year to recognise ministers in civil partnerships.
Yesterday's vote seeks to reflect Scottish law which now allows people in civil partnerships to get married.
Very Revd John Chalmers, the Principal Clerk of the Church of Scotland General Assembly, told Premier: "The Church of Scotland has maintained as its default position the traditional understanding of marriage.
"We've made room for people of a different view and in a broad church you have to do that, and perhaps we've given the denominations of the world a steer on how this can be done.
"This does not affect our understanding of what holy matrimony is in terms of our theology. So it's an interesting place for us to be.
"I hope that people will stay calm and that those who're upset by the decision - hold on there, and wait to see how this plays out."
Listen to Premier's Aaron James speaking to Very Revd John Chalmers:
