The Rhode Island Democrat told NBC-TV's "Today" show that he felt great in his recovery from substance abuse and was determined not to let the disease "take its toll on me ever again."
Kennedy checked into the Mayo Clinic in Minnesota last May after the car crash, saying at the time that he had also been at the clinic the previous Christmas. He said only that he was addicted to "pain medication" and did not name OxyContin.
Kennedy has been open about his struggles with mental illness, including bipolar disorder and addictions to alcohol and other substances. He said it didn't matter what substance he was addicted to.
"Even though I had detoxified from pain medication, one thing you learn as an addict is you can substitute anything for your main addiction," Kennedy said.
Kennedy said Friday that his public profile helped him after he checked into rehab because it has prompted other recovering alcoholics and addicts to approach him. Still, he acknowledged being hesitant to admit his addictions publicly because he said he felt ashamed.
"I am also feeling that same sense of stigma in my life, and that's why I can empathize with millions of Americans who feel that sense of shame at calling themselves addicts and alcoholics," Kennedy said.
Kennedy appeared with Rep. Jim Ramstad to promote legislation that requires equal health insurance coverage for mental and physical illnesses. Ramstad, a Minnesota Republican, is a recovering alcoholic and is Kennedy's sponsor in recovery.
After spending a month at the Mayo Clinic, Kennedy pleaded guilty to driving under the influence of prescription drugs and was re-elected to a seventh term in November.