Williams cracked at the Annual Caddie Awards dinner in Shanghai that his controversial remarks at the Bridgestone Invitational were meant to stick it to Woods, who he referred to as "that black (blank)."
"I apologize for comments I made last night at the Annual Caddie Awards dinner," Williams said in a statement posted on his Web site. "Players and caddies look forward to this evening all year and the spirit is always joking and fun. I now realize how my comments could be construed as racist."
Williams extended the apology personally to Woods. The two had worked together in Woods' heyday, but Williams was let go in July as Woods continued to struggle on the links.
Williams caddied for winner Adam Scott at the Bridgestone and raised some eyebrows in the media for what was seen as a little too much celebrating on Williams' part.
Britain's Daily Telegraph said Woods' agent called the comment "regrettable" but added Woods wasn't present in China and had no comment on the matter.