Anderson, who is the youngest artist to be exhibited at the National Portrait Gallery, is known for an acclaimed posthumous portrait of Amy Winehouse.
Profits from the sale of the painting will go to a charity called Falling Whistles that campaigns for peace in the Congo.
In a statement to Art Below, the gallery selling his portrait, Andersson explained that he felt personally connected to Jolie's experience.
"My mother had aggressive breast cancer when I was 15," Andersson said. "The recent news about Angelina stirred an anxiety within me leading me to paint this portrait."
"There is an underlying awkwardness in her demeanor in juxtaposition to the natural beauty of her face," he added.