The trooper was not hurt and investigators believe the wrong-way driver was drunk.
Washington State Patrol Trooper Julie Judson said the driver was spotted going west in the Eastbound lanes of 520 just after midnight.
Two cars collided while trying to avoid the wrong-way driver, but no one was hurt in that crash.
The wrong-way driver then crashed into Trooper Andrew Boyer near Montlake before speeding off again.
"He then drove past me very, very slowly," Boyer said. "I pretty much stared right at him as he drove right past me. He just had a very blank look on his face."
After hitting Boyer's patrol car, the driver got onto the southbound lanes of Interstate 5 going the wrong direction, but his heavily-damaged car finally gave out just north of the Ship Canal Bridge.
The 26-year-old Seattle man ran from the car and jumped over a barrier near NW 42nd Street and fell about 20 feet, Judson said.
"He didn't realize it would be quite a fall," she said.
Seattle police captured the driver and he was taken to Harborview Medical Center to be checked out.
After he is released from the hospital he will be booked into jail for investigation of DUI and hit and run, Judson said.