Michael David Barrett faces federal charges of interstate stalking for taking the videos, posting the videos online and trying to sell them to celebrity Web site TMZ, the FBI said in a statement. He was arrested at Chicago's O'Hare airport Friday night, according to the FBI.
Barrett will stay in custody until Monday, at which point the court will decide if he will travel on his own or in custody to California, where the charges were filed by TMZ, and where he will stand trial.
Barrett retained his own counsel. The maximum penalty is five years in prison and a $250,000 fine.
Barrett, 47, was arrested after returning from a trip to Buffalo, N.Y., authorities said.
Seven of the eight videos posted online were taken through a modified door peephole while the 31-year-old Andrews was alone and undressed in hotel rooms in Nashville, Tenn., in September 2008. Investigators believe the eighth video was taken in a hotel in Milwaukee in July 2008.
Several TV networks and newspapers aired brief clips or printed screen grabs from a blurry five-minute video in July.
FBI agents believe Barrett requested a Nashville hotel room next to Andrews' and rigged the door's peephole.
Barrett tried to sell the videos to TMZ under a pseudonym, but the FBI linked him to the e-mail account that was used, according to the complaint.
Barrett has never been in trouble with the law before, and friends had volunteered to help him secure bail, according to his attorney.
"I don't think he's even had a traffic ticket,'' said his lawyer, Rick Beuke, who said he has known Barrett for a decade.
"He's as regular a guy as you'll ever meet -- a great friend," Beuke added. "I must have calls from 30 people wanting to know what they could do to help."
Beuke said Barrett has been divorced for some time and has children. A neighbor in Westmont, Srividhya Viswanath, 36, a homemaker, said Barrett lived quietly in a townhome complex with a female companion. She said she never got to know them well in part because they traveled frequently. Westmont is about 20 miles west of Chicago.
A spokeswoman for the Combined Insurance Company of America confirmed that Barrett was an employee who worked in sales management. Amy Burrell-Tichy said the company was cooperating with the FBI.
An ESPN spokesman contacted early Saturday said he wasn't aware of the arrest and the network would comment later that day.
Andrews has covered hockey, college football, college basketball and Major League Baseball for the network since 2004, often as a sideline reporter during games.
A former dance team member at the University of Florida, Andrews was something of an Internet sensation even before the videos' circulation. She has been referred to as "Erin Pageviews" because of the traffic that video clips and photos of her generate, and Playboy magazine named her "sexiest sportscaster" in both 2008 and 2009.
Andrews, in an appearance on "The Oprah Winfrey Show" last month, said she thought her career was over once the nude footage of her began circulating on the Internet.
"I kept screaming: 'I'm done. My career is over. I'm done. Get it off. Get it off the Internet,'" she said as she remembered talking to her father. "They thought I was physically injured, (that's) how bad I was screaming."
Andrews has said through her attorney that she plans to seek criminal charges and file civil lawsuits against the person who shot the video footage and anyone who publishes the material.