USA Gymnastics said Karolyi died Friday. No cause of death was given.
Karolyi and wife Martha trained multiple Olympic gold medalists and world champions in the U.S. and Romania, including Nadia Comaneci and Mary Lou Retton.
"A big impact and influence on my life," Comaneci, who was just 14 when Karolyi coached her to gold for Romania at the 1976 Montreal Olympics, posted on Instagram.
The Karolyis defected to the United States in 1981 and over the next 30-plus years became a guiding force in American gymnastics, though not without controversy. Bela helped guide Retton - all of 16 - to the Olympic all-around title at the 1984 Games in Los Angeles and memorably helped an injured Kerri Strug off the floor at the 1996 Games in Atlanta after Strug's vault secured the team gold for the Americans.
Karolyi briefly became the national team coordinator for USA Gymnastics women's elite program in 1999 and incorporated a semi-centralized system that eventually turned the Americans into the sport's gold standard. It did not come without a cost. He was pushed out after the 2000 Olympics after several athletes spoke out about his tactics.
It would not be the last time Karolyi was accused of grandstanding and pushing his athletes too far physically and mentally.
During the height of the Larry Nassar scandal in the late 2010s - when the disgraced former USA Gymnastics team doctor was effectively given a life sentence after pleading guilty to sexually assaulting gymnasts and other athletes with his hands under the guise of medical treatment - over a dozen former gymnasts came forward saying the Karolyis were part of a system that created an oppressive culture that allowed Nassar's behavior to run unchecked for years.
Still, some of Karolyi's most famous students were always among his staunchest defenders. When Strug got married, she and Karolyi took a photo recreating their famous scene from the 1996 Olympics, when he carried her onto the medals podium after she vaulted on a badly sprained ankle.