Simpson was infamously found not guilty of the double homicide in 1995.
Fox showed clips of the 2006 interview in a two-hour special on Sunday night.
The interview was recorded to promote his book - If I Did It. Both the interview and the book were pulled at the time because of public outrage.
The book was eventually published after a court awarded the rights to victim Ron Goldman's family, who had won a successful civil wrongful death claim against him.
They released the book as If I Did It: Confessions of the Killer with the "If" disguised in the design.