In a heartfelt tribute to the Sex And The City actor, Burton revealed that her White Collar co-star had recently completed the book and had asked her to help his family publish it “for his son Nathen”.
Garson was a single parent who adopted Nathen, now 20, when he was seven.
Burton described Garson’s memoir as a “love letter” to the showbiz industry, storytelling, and everyone he had ever worked with over the course of his storied career.
She wrote on Instagram: “To Willie’s family, especially Nathen Garson,…on my honor, I will see it through. You have been so generous in sharing him with the rest of us.”
Burton shared that Garson first spoke to her about the memoir – which is described as “an accounting of his career as a character actor” – in 2019.
She continued: “As someone who benefited from hours of Willie’s stories over countless dinners, I loved this idea.”
The 39-year-old, best known for her role as Peyton Sawyer on American teenage drama One Tree Hill, also posted a picture of a tattoo she got in Garson’s honour before the last time that she saw him.
Explaining the significance of the words “calm down” tattooed on her arm, Burton wrote: “He would pay you the biggest compliment in the world. Tell you that you were the smartest or prettiest or most talented or that your book/show/recipe/charity, etc mattered and was valuable.
“And right as you’d blush, he’d temper it with ‘alright, calm down!’ And then laughter. He’d stop you before you could rebuff the compliment. Calm down. I can hear him saying it.”
Access unlimited streaming of movies and TV shows with Amazon Prime Video Sign up now for a 30-day free trialSign up
Burton’s husband, the actor Jeffrey Dean Morgan, commented on her post, writing: “Hard to ‘calm down’ today. We are trying.”
Burton and Garson first met on the set of USA Network’s White Collar, which aired from 2009 to 2014.
Their co-star Matt Bomer (who played charming con man Neal Caffrey) remembered Garson as “someone who lifted me up, who made me better, and who always, always made me smile”.
While actor Titus Welliver from detective drama Bosch was among those who first broke the news of Garson’s death, Nathen subsequently confirmed his father’s death on Tuesday (21 September) via Instagram.
Tributes to the late actor have continued on social media as the actor’s friends and fans remember him.
Garson’s Sex and the City co-star Sarah Jessica Parker recently wrote that she is “not ready” to mourn his death.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies