The men had been riding together in a remote forest area near the city of North Bend, around 30 miles from Seattle, when they encountered the animal on Saturday morning.
Police said the animal pounced, mauling the first cyclist and inflicting deep scratches before fleeing, only to return and fatally wound his friend.
“He jumped the first victim and attacked him,” said Sergeant Ryan Abbott, of the King County Sheriff's Office.
“The second victim turned and started to run away. The cougar saw that and went after the second victim.
“The first victim saw his friend being pulled by the cougar. He got on his bike and started to bike away.”
Police said the injured man rode for roughly two miles before getting mobile phone coverage and calling 911.
Sgt Abbott said when rescuers arrived it took around 30 minutes to locate the second victim, who was dead with the cougar standing on top of him.
Local police opened fire on the animal, which caused it to run away.
Officers from the Washington Department of Fish and Game tracked the cat through the forest for several hours before finally locating it and shooting it dead.
Neither man involved in the attack has been named, although police said the survivor, understood to be in his 40s, was taken to hospital with serious, but not life-threatening, injuries.
Rich Beausoleil, the state’s official bear and cougar specialist, said the death was only the second caused by cougars in Washington in the last 94 years.
“But it's one too many,” he added.
Fatal cougar attacks are extremely rare in North America, with less than 25 recorded in the last century, most of them involving children.
Cougars are the fourth largest cat species in the world. An adult female can weigh up to 10 stone (64 kilos), while males can weigh as much as 15-and-a-half stone (100 kilos).
Usually ambush hunters, the animals are not normally known to attack humans unless they are cornered.
Additional reporting by Reuters