Shawn D. Gulseth, 44, was charged in connection with the slaying of 45-year-old Bonnie Peterson, who was found stabbed to death in her East Kent apartment on Dec. 21, 2011.
Detectives believe the two had a romantic relationship prior to the attack.
Gulseth fled the area after the killing and was captured about three weeks later in Northern California.
He has previously been convicted for theft and drug violations, and he also stole a police car in 2005 and led officers on a wild chase through West Seattle.
Gulseth will be sentenced next month. He's facing a sentence range of 26 to 35 years, and prosecutors say they'll request 35 years.