Judges praised his "trademark mix of character comedy, anarchic stagecraft and a fearless level of audience engagement".
Andrew Maxwell, Josie Long, Sam Simmons, Nick Helm and Chris Ramsey were others nominated for the top prize.
The prizes were presented by last year's Best Comedy Show winner Russell Kane and by musical performer and 2002 nominee Omid Djalili.
Lee Evans, Steve Coogan and Al Murray are all previous winners.
Nica Burns, producer of the Foster's Edinburgh Comedy Awards, said "Congratulations to Adam Riches, who is utterly original, extremely funny and a huge talent".
He will no doubt be seen on your television screens in the near future.
