Elizabeth's father, Ed Smart, told People magazine the groom was a "very nice man" and the big event was slated for July 1.
"She told us at home last Saturday," Smart said. "I wasn't really surprised. They've been very happy together."
People said a bridal registration at Pottery Barn listed a Utah couple as Elizabeth Smart and one Matthew Gilmore.
Elizabeth Smart was kidnapped from her Salt Lake City home in 2002 when she was 14 and spent nine months as the captive of a transient couple before police found her by chance on the streets of nearby Sandy.
Smart, a music student at Brigham Young University, provides reporting and analysis for ABC News on issues related to missing and exploited children, ABC News said.