A judge quickly found them in contempt and ordered them to turn over the tape by Wednesday at 2 p.m.
Edwards' mistress Rielle Hunter went to court to get the tape that reportedly shows her and Edwards having sex.
Hunter was not at the hearing Friday.
Young, a former aide to Edwards, said he and his wife found the tape after Hunter moved out of their house in 2007. Edwards has publicly admitted to beginning an affair with Hunter in 2006 while she worked on his campaign as a videographer. He has also admitted to being the father of her daughter.
The existence of the video came to light after the publication of Young's new book "The Politician," in which he chronicles the Edwards affair and his involvement in trying to keep it secret.
In court filings, Hunter demands the Youngs to turn over the tape and any copies saying it depicts "matters of a very private and personal nature."
She also wanted several photographs.
Deputies went to retrieve the materials, but Young's attorney told the authorities he could not immediately turn over the items.
In their written response ahead of Friday's court appearance, lawyers for the Youngs argued they shouldn't be forced to give the tape up.
But Friday, Judge Abe Jones told them if they didn't, he could put them in jail.
"Please comply so we don't have to go to the next step," said Jones.
According to an affidavit filed by Young Friday night, the original sex tape is in an Atlanta safety deposit box along with possibly two other copies. The judge has asked for all of the copies Young has.
Young also said another copy has been turned over to the FBI, which has been investigating the money that exchanged hands during Edwards' second White House campaign.
He also said in his affidavit that he would turn over campaign videos and photographs shot by Hunter.
Judge Jones said once the tape and photos were produced. He would put it under lock and key until the issue of who owns them is resolved.
Young told reporters after the court hearing that he and his wife, Cheri, were happy to comply and supply the items. He has previously said that he kept the tape as security and proof of his story while declining large financial offers for the video.