The penalty phase is scheduled Tuesday for 65-year-old John Nordstrom III of Austin. He faces up to life in prison.
Prosecutors in Austin say Nordstrom on Monday pleaded guilty to murder over the shooting death of 58-year-old Deborah Diane Gordon.
The Austin American-Statesman reports police were summoned on Aug. 30, 2010, after one of Nordstrom's sons stopped at the house and noticed a suspicious odor.
The woman's body was on a couch, covered by a sheet. Investigators believe Gordon was killed Aug. 5.
Police say Nordstrom tried to make it look like his wife committed suicide and he kept neighbors and other visitors away from their home.