Authorities said 18-year-old Kelsey Smith's body was found across the state line at a lake in Grandview, Missouri.
Overland Park Police Chief John Douglass identified the suspect as Edwin R. Hall, 26, of Olathe. He was expected to be charged Thursday with premeditated first-degree murder and aggravated kidnapping.
Douglass said Hall was interviewed Wednesday after police acted on a tip that matched Hall and a vehicle to surveillance video from the Target store parking lot where Smith was abducted Saturday evening.
Smith's body was found about 1:30 p.m. Wednesday, about 20 miles east of the abduction site.
In a statement released to the media after the arrest was made public, Smith's parents said, "we would like to thank the law enforcement community for their hard work… We are pleased that an arrest has been made."
Douglass declined to comment on the circumstances of Hall's questioning or evidence in the case, but said police had located a vehicle that matched the description of one seen in surveillance video pulling into the Target parking lot about a minute after Smith parked there.
He said Hall appeared to be the same person shown in the video walking into the Target soon after Smith entered the store.
Smith, who graduated from high school less than two weeks ago, was seen on a security video leaving the store around 7:10 p.m., then putting packages into her car when someone ran toward her, police said.
"You see two individuals come together, and there is no separation of those two individuals," Douglas said. "So it is easy to conclude there was some kind of incident at the back of the car. Then the car leaves."
Johnson County prosecutor Phill Kline said charges would be filed Thursday morning.
"This community has lost a vibrant and promising life and her family has suffered unimaginable tragedy," he said.
Kline said his office would ask the state to set bond at $5 million.
Hall faces a 25 year minimum sentence on the premeditated murder charge, and Kline said his first court appearance could come as early as Thursday, but will more likely be on Friday.