Monday was the deadline for Brian David Mitchell to appeal his conviction of kidnapping and rape of the 14-year-old he took at knifepoint from her home in Salt Lake City.
A jury convicted Mitchell in December. He was sentenced to two life sentences.
"It's nice to see the defense do the right thing for a change," Smart told the AP on Monday.
Her father, Ed Smart, said Mitchell's decision not to appeal brings finality to the entire case.
"I'm grateful that he's not appealing," Smart said. "We've felt pretty good since the trial that things were going to come out this way. It's good to now be at this point where things are what they are and it's not going to be fought."
Smart, who is now 23, testified that her kidnapping was "nine months of hell" in which she endured daily rapes, lived homeless and was forced to use drugs and alcohol.
The Associated Press contributed to this report.