From Spanish to English, "Me siento bien" can be translated as "I feel well" or "I feel good." Native English-speaking Americans hardly make any distinction between the two. We have long since confused the proper grammar and use of the words. If you really want to be proper, then yes, "I feel well" is the accurate way to say it. But most people don't care and most use "well" and "good" interchangeably. I would think that a majority of English-speakers say "I feel good" anyway.

"Bien" translates as "well." "Buen" as "good."

Bien/well are adverbs, which means that they modify verbs, adjectives, or other adverbs. An adverb tells how something is done.

Buen/good are an adjectives, which means that they modify nouns. An adjective tells a trait of a noun.

"I am well" or "Me siento bien" is correct because well/bien tells how one feels. If we use "I am good" or "Soy/estoy bueno", that would imply "I am morally good", or something along those lines.

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The issue is not that we say "I feel good." That's just spoken English. The problem is that in Spanish "bien" and "bueno" have not been confused as they have in English, so in translation, we have to be careful.

In Spanish we don't have a clear diferentation between "I feel good" or "I feel well", both can be translated as "Me siento bien", We don't have the construction "Me siento bueno". It doesn't happen the same with others verbs "estoy bien" or "estoy bueno" has different means as I am well or good in English.

I never know if it is "good" or "well" when I seen "bien" or "buen". What is the difference? This may explain it: http://data.grammarbook.com/blog/adjectives-adverbs/good-v-well/ "When referring to health, always use well"