In further alarming videos posted publicly, Stephens allegedly claimed to have killed 13 people and said himself to be "working on 14".
After a brief, 2-mile traffic pursuit, Stephens pulled out a handgun and killed himself, Reed said.
Stephens was wanted on an aggravated murder charge in the shooting death of a 74-year-old man who was picking up aluminum cans on Sunday after spending Easter with his family.
The video of the shooting was not broadcast live.
The manhunt for Stephens had expanded nationwide on April 17.
The victim was identified as 74-year-old Robert Goodwin Sr.
According to GoErie.com, he died of a self-inflicted gunshot wound in a white Ford Fusion near Buffalo Road and Downing Avenue just after 11 a.m. Tuesday.
The head of the U.S. Marshal's office in Cleveland says he's confident Stephens will be found. And when it stopped, officers approached the vehicle as Stevens took his own life, Williams said. Stephens, who goes by the name Stevie Steve on Facebook, recorded an encounter with Godwin on Sunday.
Police say Stephens had a permit to carry a concealed weapon.
The multistate manhunt for him stretched into a third day Tuesday.
Police are on alert, including in NY, as a manhunt for the man accused of killing a stranger in Cleveland and posting a video of it on Facebook is now entering its third day.
Steve Stephens, the Cleveland murder suspect accused of posting video of the killing on Facebook, was found Tuesday in Erie County, Pennsylvania, state police said on Twitter.
Other videos Stephens shared show him talking about his despair over gambling debts and trouble with his girlfriend.
A source close to Facebook says it has "thousands" of people reviewing content around the world. "As a result of this bad series of events, we are reviewing our reporting flows to be sure people can report videos and other material that violates our standards as easily and quickly as possible", Justin Osofsky, Facebook's vice-president for global operations, said in a statement.