The MSP, who is gay, praised her colleagues for the mature debate that led to the Marriage and Civil Partnerships (Scotland) Act, becoming law, and said that the Scottish Parliament "rose to the occasion".
Scotland became the 17th country to allow gay marriage on Tuesday when the bill was passed by 105 to 18 votes, despite opposition from both the Church of Scotland and the Catholic Church.
Ms Davidson wrote in the Sunday Herald: "Growing up in a small village in the East Neuk of Fife, it was a day I never thought I'd see in my lifetime - never mind be a part of - and it was, without question, one of the proudest days of my life.
"I am not ashamed to say that on returning to my parliamentary office after the vote, I cried deep sobbing tears of relief and release and joy and pain and pride and dozens of other emotions all mixed up together.
"It felt (and still feels) like we had just changed the world for the better, and what we had done could now never be undone. It felt that big." The MSP added that the new law would end years of discrimination against homosexuals and that it created a fairer society where "marriage was valued equally and would be open to all".
She said: "Knowing that the Scottish Parliament had stood up for them, young gay people could walk taller into the playground the next day with the courage to face their accusers down."