Katona was secretary-general of the János Bolyai Mathematical Society from 1990 to 1996. In 1966 and 1968 he won the Grünwald Prize, awarded by the Bolyai Society to outstanding young mathematicians, he was awarded the Alfréd Rényi Prize of the Hungarian Academy of Sciences in 1975, and the same academy awarded him the Prize of the Academy in 1989. In 2011 the Alfréd Rényi Institute, the János Bolyai Society and the Hungarian Academy of Sciences organized a conference in honor of Katona's 70th birthday.
Gyula O.H. Katona is the father of Gyula Y. Katona, another Hungarian mathematician with similar research interests to those of his father.