The purchase price was not disclosed.
"The building is being considered for church operations, possibly as an audio/visual studio or warehouse," said LDS Church spokesman Scott Trotter.
The 67,000-square-foot building sits on 8.4 acres north of I-80 and just west of the south end of the Salt Lake City International Airport.
Greg Miller, chief executive officer of the Larry H. Miller Group, which also owns KJZZ and the Utah Jazz, described the sale as "a win-win deal."
KJZZ had consolidated its broadcast operations to the EnergySolutions Arena and moved out of its former studios during recent months.
"The building was sitting dark and vacant," Miller said. "As a family, we wanted to do all we can to preserve that facility."
That meant the family wanted the building's studios and broadcast accent to remain intact.