You are eligible for Medicare at age 65. There is no provision in Medicare to be "on" someone else's benefit. You will have to pay the monthly premium like us who have paid in for our entire working careers. Since your wife is eligible for Medicare, you are also:
From Medicare's site:
Most people age 65 or older who are citizens or permanent residents of the United States are eligible for free Medicare hospital insurance (Part A). You are eligible at age 65 if:
- You receive or are eligible to receive Social Security benefits; or
- You receive or are eligible to receive railroad retirement benefits; or
- Your spouse is eligible; or
- You or your spouse (living or deceased, including divorced spouses) worked long enough in a government job where Medicare taxes were paid; or
- You are the dependent parent of a fully insured deceased child.
If you do not meet these requirements, you may be able to get Medicare hospital insurance by paying a monthly premium. Usually, you can sign up for this hospital insurance only during designated enrollment periods.