Edwin R. Hall, 26, was expected to be charged Thursday morning with premeditated first-degree murder and aggravated kidnapping, Overland Park Police Chief John Douglass said.
Kelsey Smith, 18, had been missing since Saturday night, when she went to a Target store in this Kansas City suburb to buy a gift for her boyfriend.
Surveillance video showed her being forced into her car around 7:10 p.m., and the car drove off. It was found in a nearby mall parking lot about two hours later.
Douglass said Hall appeared to be the same person shown in the video leaving the Target soon after Smith. He was wearing a white T-shirt, sneakers, shorts and a goatee.
"This community has lost a vibrant and promising life and a family has suffered unimaginable tragedy," said Phill Kline, prosecutor for Johnson County, Kan.
Police said Hall's vehicle matched the description of a dark mid-1970s Chevrolet pickup that was seen entering the Target parking lot shortly after Smith's car.
"I want to again express my condolences to the Smith family," Douglass said. "I realize that this is not the preferred conclusion. While we cannot give them their daughter back, we can at least give them justice."
Douglass said police had received more than 500 tips in the case and had questioned numerous people, including Hall, who was arrested at the end of his interview Wednesday.
Douglass said there was no evidence that Hall and Smith knew each other. He declined to offer a motive for the attack or specify whether investigators had determined that Smith was killed in Kansas, where the murder charge was to be filed.
Police found Smith's body in a wooded area near Grandview, Mo., about 20 miles east of the Target store. Authorities did not say how she died.
"As I understand she was found at a wooded area, but I can't say whether she was directly concealed by bushes," Douglass told reporters.
Officers had been searching the lake area since Tuesday after tracing signals from Smith's cell phone. Investigators isolated two signals from an area in south Kansas City, Mo.
Before a memorial service Wednesday evening, Smith's father, Greg Smith, thanked the hundreds of volunteers and everyone else involved in the search for his daughter.
Smith remembered his daughter as a young woman "scrubbed in sunshine," reports CBS News correspondent Cynthia Bowers.
"She could walk into a room full of strangers and walk out with a room full of friends," Smith told the gathering, fighting tears.
"Her excitement and passion for life was unmatched," he said. "She lived more in 18 years than many people do with a great deal more time."
After his daughter's body was found, Kimberly Kincade, 39, was one of only a few people who remained at the makeshift staging area for searchers in the Target parking lot, surrounded by stacks of fliers and cases of water and soda.
"The person who is going to keep us the strongest is Kelsey," Kincade said, fighting tears. "She's up there looking down and saying, 'I know this is bad, and I know that I'm not there with you anymore. I can't hold you, and I can't hug you. But both of my arms are wrapping around you, and I'm there with you."'