She was last seen on Jan. 17 when she left her in-laws' house in Garden Ridge for a walk, CNN reported.
A passerby found the body at 12:15 p.m. Thursday in a wooded area near his home, city police chief Donna O'Conner said.
"We will reserve any information regarding the cause of death until an autopsy has been performed," the chief said. "Our thoughts are with the Bearden and Hecht families."
Bearden, 33, and her husband, Josh Bearden, had been traveling for 22 months before her disappearance.
They returned to the United States in December, and her family members said the transition was difficult for Leanne Hecht Bearden.
Widespread searches were conducted, but at the time, police said her disappearance did not appear to have a criminal element.
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