Simmons topped a shortlist that also included four-time nominee James Acaster, as well as Joseph Morpurgo, Kieran Hodgson, Nish Kumar, Sarah Kendall, Seymour Mace and Trygve Wakenshaw.
Awards producer Nica Burns said: “Sam Simmons has funny bones. He is a complete original, combining physical comedy with great verbal jokes and a unique take on life.
“His 2015 Edinburgh show is outstanding. This is a comedian at the top of his craft who has grown substantially since his two earlier nominations.”
The Best Newcomer prize went to Sofie Hagen, who Burns described as “a young comic with an effortless engaging style”.
The discretionary panel prize was given to Gilded Balloon founder and artistic director Karen Koren, who is stepping down after a 30-year tenure.
Sky’s head of comedy Lucy Lumsden, who chaired this year’s panel, said: “Karen Koren encapsulates the true spirit of the fringe in so many ways. Entrepreneurial, warm-hearted, a great survivor and a huge supporter and spotter of new talent.”
Simmons takes home a prize of £10,000, while Hagen and Koren win £5,000 each.