Stern, 40, who was separated from the former Deal or No Deal model, shot himself on Sunday, a family spokesperson confirmed to PEOPLE in a statement.
"On Sunday, June 22, Andrew Stern, husband of Katie Cleary, committed suicide at a shooting range in the San Fernando Valley," the statement said. "Andrew and Katie have been in the midst of a very amicable separation and had remained on excellent terms. This is devastating news for us but we have been aware of Andrew's longtime struggle with depression."
Cleary, 32, who was also a contestant on America's Next Top Model, was photographed in Cannes in May with Leonardo DiCaprio, but the family spokesperson tells PEOPLE that "any rumors of any kind of extra-marital relationship are entirely fabricated and completely false," adding that Cleary's interaction with the Oscar winner "was fully for the purpose of potential collaboration for environmental and animal welfare issues."
A public memorial service for Stern will be held on Saturday in Venice, California.
Reporting by MELODY CHIU