The animal attacked the two men as they were on a morning bike ride in the hills near the city on Saturday.
It is believed to be the second cougar fatality in Washington state in nearly 100 years.
Police said the cougar lunged at the man who survived the attack first. As the other man attempted to run, the animal turned its attentions to him, giving chase and pouncing on him before pulling him away.
The first man then escaped on his bike, riding for two miles before finding mobile phone coverage and calling for help.
When authorities returned to the scene of they found the cyclist dead, with the cougar standing on top of his body.
The animal ran off but was discovered in a tree and killed several hours later. Rescuers had to wait to retrieve the man’s body while the cougar was being hunted.
Sometimes known as pumas or mountain lions, cougars can be found across South and Central America and in mountains and forests to the west of the United States.
They are a protected species in the US, but every year Washington state allows 250 of the animals to be hunted and killed in 50 designated zones.
The man who survived the attack is said to be hurt but in a stable condition in hospital.
Rich Beausoleil, the state’s bear and cougar specialist, said it was only the second fatality in the state in the last 94 years, but that was still “one too many”.