The attack happened around noon on March 12. Investigators said the 35-year-old woman had just finished jogging when a man grabbed her from beind and tried to sexually assault her.
The woman was able to fight off her attacker and escaped by jumping off the edge of a cliff into the water below.
Deputies said the suspect did not follow the woman into the water, but stole her Toyota Land Cruiser and fled the scene.
The victim was treated at a hospital for cuts and bruises.
Deputies said Verdin was arrested after detectives matched his DNA with material found at the crime scene. Verdin was a known drug user and was on parole for a burglary in 2008.
"He's been a convicted felon and due to the felony arrest his DNA was obtained," said Detective Tom Lewis of the Los Angeles County Sheriff's Department.
Lewis said it is believed the Verdin used a weapon during the attack, however nothing was recovered from the scene. The victims SUV also remains missing.