Rev Dr Martin Fair, 55, who will take up the role next May, said he was "devastated" by the singer's death and felt he had to take action.
He led the rollout of three services by Havilah, the social action project of his congregation at St Andrews Parish Church in Arbroath, Angus.
Dr Fair said: "Suicide is a horrendous endemic problem and we decided, as a church, that we had to do something.
"I have buried too many people who have taken their own lives over the years because they felt alone and helpless in the darkness which many think is their only friend.
"I am a big fan of Frightened Rabbit and was absolutely devastated by Scott's death.
"When his body was found something snapped within me and I decided that I could not go on merely saying 'isn't it terrible' every time someone took their own life."
The singer's body was found at Port Edgar near South Queensferry on May 10 2018 after he was reported missing.
Open five days a week, Havilah now offers a drop-in service, community choir and a therapeutic garden in addition to addiction support services.
The new services were designed by congregation members - three mental health professionals and three people who have struggled with their own mental health.
Since being set up by Dr Fair and the congregation in 2006, Havilah has helped around 1,000 people.
Dr Fair called for more investment in mental health services.
"The statutory provision to support people with drug additions and mental health is desperately short in terms of what is needed to address the epidemic," he said.
"Churches and the wider voluntary sector have an obligation to step in and fill the gaps until they are able to access the appropriate services."
Dr Fair, who was ordained and inducted into St Andrew's Parish Church in 1992, hopes to highlight addiction and mental health issues during his year in office.
He will take over from the current moderator the Right Rev Colin Sinclair and will be the first moderator from Arbroath to serve as the Kirk's ambassador at home and abroad during what will be the 700th anniversary year of the Declaration of Arbroath.
Dr Fair was brought up in Spiersbridge Church, now called Thornliebank Parish Church, in Glasgow, and believes claims the Kirk is in its "death throes are well wide of the mark".
"As I travel round the country even now, I see green shoots of growth and live in hope for what is going to come," he added.
Dr Fair said he is excited and a bit daunted about becoming moderator and his one regret is that his parents, Ena and Bill who were born and bred in the Church, did not live long enough to see him take up the post.
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