Depp, 49, started a relationship with Heard, 26, a few months back, after separating from long-time partner Vanessa Paradis, reported Sun online.
"Buying this house is the surest sign yet of how serious Johnny is about Amber," a source said.
"She has always dreamt of having a ranch. They were going to buy one in Texas, where she's from, but they fell in love with the Nashville property as soon as they set eyes on it," the source added.
"Johnny isn't bothered about living it up in Hollywood, he would rather have the good life. While Amber loves to ride horses, Johnny's serious about writing and playing music," the source said.