The newspaper cited unnamed sources at the Cleburne County Sheriff's department in Arkansas as saying the singer, songwriter and music producer died of a self-inflicted gunshot wound Sunday night.
The Post did not say what part of his body he shot. It also didn't suggest why he apparently committed suicide.
Wilson, 34, is the father of McCready's 9-month old son. He also helped the singer raise her 6-year-old son from a previous relationship.
"Today, we mourn the loss of my life partner and my children's father, David Wilson," McCready said in a statement to the FOX411 entertainment blog. "David was my soulmate; he was a caregiver and guiding hand to our sons, Zander and Zayne. He was a precious gift from God to all of us and, yesterday, he returned home and is now with his mother and father."