Zou, who won China's first Olympic boxing medal, a bronze, in Athens and its first gold at the Beijing Games, beat Thailand's Kaeo Pongprayoon in London to become the first light-flyweight to win three Olympic medals.
Arum's stable of fighters also includes eight-division world champion Manny Pacquiao and WBO welterweight title holder Timothy Bradley.
"Zou is an incredible talent who is beloved in the People's Republic of China," Arum said in a statement on Wednesday. "We at Top Rank will make every effort to make certain that he has a spectacular career as a professional boxer."
The 31-year-old Zou also captured gold medals in the World Amateur Championships in 2005, 2007 and 2011.