"My actions at the 94th Academy Awards presentation were shocking, painful, and inexcusable," his statement said.
The Academy said it accepted the resignation and would "continue to move forward" with disciplinary proceedings.
Smith slapped Rock over a joke about his wife's shaved head, a result of the hair-loss condition alopecia.
Less than an hour later, he was awarded the best actor award for his role in "King Richard", where he played the father of tennis stars Venus and Serena Williams.
"The list of those I have hurt is long and includes Chris, his family, many of my dear friends and loved ones, all those in attendance, and global audiences at home," Smith said on0 Friday.