The 37-year-old was being hunted by the Pennsylvania State Police after he murdered Robert Godwin Sr, 74, over the Easter weekend.
"There was a short pursuit in which the vehicle was stopped. As the officers approached that vehicle, Steve Stephens took his own life," Cleveland police chief Calvin Williams said.
“We would prefer that it had not ended this way, because there are a lot of questions I’m sure that not only the family but the city in general would have had for Steve, as to why this transpired.”
Stephens was wanted for murder after he uploaded a video onto Facebook which showed him shooting Godwin in the head.
Stephens, who did not know the victim, said in the video: "Here’s somebody I’m about to kill. I’m about to kill this guy right here. An old dude."
The video stayed up for three hours before it was removed by Facebook.
Godwin’s family pleaded with the public to stop sharing the video.
“Please please please stop retweeting that video and report anyone who has posted it! That is my grandfather show some respect,” Godwin’s grandson, Ryan Godwin, wrote on Twitter Sunday.
The victim's daughter Brenda Haymon said she wished Stephens had been caught.
“All I can say is that I wish he had gone down in a hail of 100 bullets,”she told CNN.
“I wish it had gone down like that instead of him shooting himself.”