As others have stated, you are definitely entitled to Medicare at age 65, if you are qualified by years of working in the U.S.
The real question, as Vadio mentions, is the level of Medicare coverage you choose, bearing in mind that when living abroad, you can only enjoy Medicare benefits if you make the trip back to the U.S.
First level; Part A, no further cost
Second level; Part B, significant monthly premium
Third level; various add-ons, such as Part D, Medicare Supplement policies, Medicare Advantage policies, etc., most with significant additional monthly premiums
(Important to note that you MUST pay the Part B in order to then take Part D, Medicare Advantage, or Medicare Supplement. AND you must take Part B every year, or there's a cumulative penalty if you decide to belatedly take it in the futur, having missed years.)
Since I divide my time between the UK and the U.S., my choice was to pay Part B premiums and to take a high deductible Medicare Advantage plan ($0 premium.) I don't really intend to use healthcare in America, but, of course, you need some sort of coverage there, in case of illness or accident while visiting...