"After leaving the governor's office, I told my wife about this event, which occurred over a decade ago," Schwarzenegger, 63, said in a statement this week. "I understand and deserve the feelings of anger and disappointment among my friends and family. There are no excuses and I take full responsibility for the hurt I have caused. I have apologized to Maria, my children and my family. I am truly sorry."
On Monday, Shriver, 55, asked for privacy and compassion.
"This is a painful and heartbreaking time," Shriver said in a statement. "As a mother, my concern is for the children. I ask for compassion, respect and privacy as my children and I try to rebuild our lives and heal. I will have no further comment."
Shriver appeared at Oprah's star-studded farewell show taping Tuesday night in Chicago.
"For more than 30 years you have bestowed upon me the most amazing friendship. You have shown love, support, wisdom, and most of all, the truth?" Shriver said at Tuesday's taping.
She paused for a moment after she uttered the phrase "the truth."