The 49-year-old coached his daughter Nastia Liukin who won the all-around gold title at the 2008 Beijing Olympics.
"Valeri has excelled as a personal coach and he has demonstrated his ability to lead and guide other coaches through his efforts as the elite developmental coordinator," president of USA Gymnastics Steve Penny said in a statement.
"He will provide a smooth transition from the programme that has been created and Valeri is recognised as a capable and talented coach."
Karolyi retired as women's team coordinator, a position she held since 2001, following last month's Rio de Janeiro Olympics.
(Reporting by Ian Rodricks in Bengaluru; Editing by Tony Jimenez)
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