This was the first time Mr Stuart returned to the country since he won the prestigious award for debut novel Shuggie Bain, a book based on his own upbringing in Glasgow.
He is now based in New York, and chatted with the First Minster about his novel, poverty, strong women, addiction and homophobia.
Ms Sturgeon explained how she reacted to his book very personally having been raised in the west of Scotland, saying: “I knew people like Shuggy, I knew people like Shuggy’s mum.
“It makes you cry, it makes you laugh, it takes you to moments of great despair but also lifts you up into optimism as well.”
Shuggy Bain’s mother in the book struggles with alcoholism and Mr Stuart explained that as his own mother also struggled with the same addiction, it was important to him to give her a voice.
He said: “I just wanted to share this story and get it out there.”
"It’s about love, its about all kinds of love.”
"Often when men suffer with addiction, they do it in public, they go to the pubs. the miners clubs, you see them on the street...but when women, when mothers suffer it can be a very secret thing for a long time.
"We often blame women harder than we blame men when they suffer.”
Ms Sturgeon mentioned the problem with addiction in Scotland, adding that the book was able to show a human side to this and helps people understand it.
She said: "It challenges the stigma of addiction...people feel like they can’t come forward for the help they need.
“Poverty and addiction...it is often women and children who suffer disproportionately.”
It was thought that the First Minister would not be able to attend the sit down interview in front of a live audience, due to being pinged as a close contact tested positive.
However, she announced that after staying at home, she has received a negative test.
The full interview can be found on the Edinburgh Book Festival website.