Gary Galcik, who created the Dysfunctional Family Circus Web site in 1995, agreed to take the site down after talking with Family Circus cartoonist Bil Keane by telephone this week.
"I'm not convinced I was on the wrong side of the law," he wrote on his Web site, but "knowing Bil was personally upset at the site, it depressed me."
He plans to take the site down Oct. 8.
Keane last week threatened legal action against Galcik, saying some of the parody captions were indecent - contrary to the wholesomeness and family values he tries to portray with his comic strip.
"He said more than anything else, he didn't want to hurt me," Keane told The Arizona Republic.
Keane, who has drawn the cartoons for 40 years, was pleased by the way the situation was being resolved.
"It has a happy ending, as everything dealing with The Family Circus should be," he said.
The Family Circus is carried by 15,000 newspapers worldwide, reaching about 100 million readers.
You can find the Dysfunctional Family Circus at the following address: http://www.spinnwebe.com/dfc/