"In his letter to us, he stated that he was suffering from acute depression and he felt it was his only way out," Hug's parents told People. "While publicly outgoing he was an extremely private person who internalized everything."
The 35-year-old's body was found in a remote area off a Southern California highway Wednesday.
Hug's family said they felt it necessary to come forward about the real cause of their son's death after false reports had surfaced in the media.
"Our son meant the world to us and this came as a complete shock," they said. "We are beyond devastated and completely distraught. ... What we saw was his thirst for life with fast cars, motorcycles and his love of skydiving."
"What we see now is the immense amount of love that everyone has for him," his parents said. "Anyone close to Julien is receiving an extreme outpouring of concern via text, email and messages. This is an honored tribute to what an amazing person he was and we thank everyone for their love, prayers and continued support."
Hug was eliminated by Jillian Harris during the second episode of the fifth season of The Bachelorette.