You can enroll in Medicare during the seven-month period that begins three months before the month you turn 65. Coverage can start as early as the month of your 65th birthday. If you don't sign up during this initial enrollment period, you could be charged higher premiums for the rest of your life. If they sign up later than 65 for Medicare, they are going to pay late penalties, says Tanya Feke, a medical doctor and author of Medicare Essentials: A Physician Insider Explains the Fine Print.