Stephens, who had no prior criminal record, was not suspected in any other killings, Cleveland officials had said.
The employee called state police as the manager and owner went to the window to give Stephens his chicken nuggets, but said his fries were going to be another minute. He shot himself in the head as the vehicle spun out of control.
Pennsylvania State Police said officers saw Stephens in Erie County on Tuesday morning.
A patrol trooper was not able to stop in time and slid into Stephens' vehicle.
"I want to officially announce that the search for Steve Stephens has ended", Cleveland Police Chief Calvin Williams told reporters at a press conference.
Police said Stephens, 37, killed 74-year-old Robert Godwin Sr.in Cleveland Sunday, then posted video of the horrific crime on Facebook. Despite initial reports, Facebook denies that it was broadcast live on its platform, claiming that Stephens uploaded the video after the shooting.
PBS NewsHour will update this story as it develops.
In a video Stephens later streamed on Facebook Live, he said he "snapped" and killed 13 people, saying "I've got a lot of built-in anger and frustration".
Federal, state and local law-enforcement agencies had launched a nationwide manhunt for Stephens, who was wanted on an aggravated murder charge.
The company on Monday said it would review how it monitors violent footage and other objectionable material in response to the killing.
Police would not speculate on what was behind the killing, but videos Stephens posted showed him talking about losing everything he had to gambling and trouble with his girlfriend.
Godwin's sister said she feels, "Angry sometimes", over Robert's death and that she was hoping Stephens would be brought to justice. "But we know we need to do better". When authorities tried to pull him over, he shot and killed himself.