The Rev Bryan Kerr's motion called for a draft of new laws to give ministers the option, nearly a year after the Scottish Episcopal Church voted to let gay couples get married in church.
The motion as amended was passed 345 to 170 at the general assembly in Edinburgh on Saturday.
Speaking ahead of the vote, the Rev Tom Gordon said: "I have two daughters, both of whom are married. I have one gay daughter in a same-sex marriage. When my older daughter got married she had a choice - to ask me to conduct her service as a minister or for me to walk her down the aisle as her dad. But when my younger daughter got married, she had no such choice.
"Give people a choice - allow their marriage to be conducted by a minister. With God's blessing."
It was amended to ensure the committee had the power to recommend withdrawal following a call from Rev Peter White of Sandyford Henderson Memorial Church in Glasgow.
A committee has been tasked with drafting a ruling and will report back by 2020.
Speaking after the vote, Rev Kerr said: "I am delighted that that the General Assembly continues on a road where we are able to say to people in same-sex relationships that the Church has a place for you.
"I am pleased we have reached this point and I have already had reaction from parents of people in same-sex relationships who are overwhelmed that the Church accepts that God loves them."
Rev Mark Malcolm, minister of Chryston Parish Church in Glasgow, is a member of evangelical Kirk group, Covenant Fellowship Scotland.
Reacting to the vote he said: "From those of us who want to uphold the traditional and orthodox teaching of the Church, it is possibly as good an outcome as we could expect.
"Looking into the future, I think what is likely to happen is instead of the default position of the Church being orthodox and traditional, it will be revisionist.
"And you will have to opt-in to the orthodox position rather than holding that position."
A final poll is expected in 2021.
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