Court documents filed Thursday say Michael Barrett will plead guilty in Los Angeles federal court.
He faces up to five years in federal prison and a fine of $250,000.
Barrett is suspected of renting hotel rooms adjacent to Andrews in three cities last year, altering the peepholes and shooting videos of Andrews in two of the locations.
Barrett is accused of uploading the videos to the Internet and trying to sell them to celebrity gossip site TMZ this year. Several TV networks and newspapers aired or published images of Andrews taken from the videos.
A week ago, the FBI at the Northern California offices of tech giants Yahoo and Google Inc. seeking additional information about Barrett and a second video of a naked woman - not Andrews - he is believed to have taken.
In an affidavit, FBI agents said they were looking for a 42-second video entitled "Hot Blonde Out of Shower," which was posted in June to Flickr.com by a user named "Breastboy." Flickr is owned by Yahoo.
Authorities believe the Flickr account belongs to Barrett, 48, of Westmont, Ill. The video, which appeared to be taken through a hotel room peephole, was viewed nearly 3,000 times before it was taken down.
Assistant U.S. Attorney Wesley Hsu confirmed the woman on the Flickr video was not Andrews but declined to elaborate. Prosecutors previously said Barrett had uploaded videos of other unsuspecting nude women to the Internet.
Both Yahoo and Google declined comment.