Gary Hartman, 66, was arrested on Wednesday and has been charged with murder in the first degree and rape in the first degree, Tacoma Police Chief Don Ramsdell said at a news conference on Friday about the cold case.
Hartman will be arraigned on Monday, CNN reported.
According to police records, Michella Welch and her two younger sisters went to the city's Puget Park on March 26, 1986.
About 11 am Michella rode a bicycle home to get lunch. While she was gone, the sisters went to a business to use the restroom, Ramsdell said.
"A search dog found Michella's body that night in an isolated area, more than a quarter mile away from the play area," Ransdell said. She was sexually assaulted and murdered.
Two brothers were identified as possible suspects and surveillance began leading to a detective follow Hartman into a restaurant when he met a co-worker for coffee, CNN quoted Ramsdell as saying.
"I observed him using the napkin multiple times," the detective said.
"He crumpled it up, put it into a bag and then crumpled that bag up and voluntarily abandoned that bag as he left the restaurant."
The napkin was collected and sent to the Washington State Patrol Crime Laboratory. On Tuesday, the lab told police the DNA on the napkin matched DNA found at the crime scene.