Turner, 21, was arrested Wednesday by police and the United States Marshall Service at the Greyhound bus station in Charleston after they received a call from Pennsylvania State Police.
Earlier in the week, the St. Johns County Sheriff's Office in Florida said Turner was allegedly seen three times in less than a day in the St. Augustine area.
Authorities said Turner resided in this section of Florida before moving to Crawford County, Pennsylvania.
Forty-nine-year-old Shannon Whitman and her 10-year-old son were found dead by family members on August 10, ABC affiliate WJET-TV reports.
Troopers tell WJET-TV that they believe Turner stole a car at the murder scene. They say he then drove it to a Kwik Fill gas station in Millcreek Township and proceeded to rob the store.
Turner is being held in West Virginia but will be returned to Pennsylvania to face charges