Adams revealed in a statement to the US magazine that the couple had decided to end their six-month relationship.
He said: "Mandy is one of those genuinely sweet angelic people you wish to meet your whole life. I am grateful for our friendship and how it allowed us both to grow and learn more."
The 33-year-old alt-rock singer cited press intrusion as a factor in their split.
He explained: "Unfortunately I am allergic to paparazzi and have found the best antidote to that sort of nonsense is staying behind the guitar and typewriter, staying close to my support group of friends and bandmates and not engaging in activities that prevent me from taking care of myself or others.
"I found the entire speculation and subsequent photographs and intrusions terrifying and only wish to live as normal a life as possible."
Moore has previously dated tennis player Andy Roddick and Scrubs actor Zach Braff.