An enforcement officer and the dogs tracked the animal after authorities were told it had been spotted Saturday night, the latest sighting in or near the 534-acre preserve, he said.
The cougar is a 2½-year-old male, weighs 140 pounds and is in very good health, Capt. Bill Hebner said.
After examining the animal, wildlife agents drove it to be released in the Cascade foothills near Skykomish, about 45 miles northeast of Seattle.
"It's a very good prospect for relocation," Hebner said. "It wasn't aggressive or stalking people, and it maintained its natural respect for the wild."
The park reopened late Sunday morning, city parks spokeswoman Joelle Ligon said.
The animal likely preyed on house cats during its time in the park, Hebner said. Earlier, he noted the heavily forested park was a perfect urban retreat for the cougar because there's no competition for the territorial animal. There's also plenty of food in the form of rabbits and other small animals, along with neighborhood pets.
The mostly undeveloped park on the city's northwest side includes miles of trails, beaches along Elliott Bay and spectacular views of Puget Sound and the Olympic Mountains. Fish and Wildlife officers believe the cougar followed a wooded rail corridor running south into the city, then crossed the Lake Washington Ship Canal over a railroad bridge to reach the park.
"He came a long ways without being seen," Hebner said, a good sign the elusive cat wants little to do with people.
Agents found a report of a cougar sighting near the park Aug. 21, so the animal probably was in the city for two weeks or more, he said.
Agents attached a GPS collar on the cougar that will automatically send updates on its location twice a day, Hebner said.
In an unrelated incident, a cougar was struck and killed by an automobile Saturday evening in Redmond, east of Seattle. The driver of the vehicle was unhurt, Hebner said.