"Grammatically Correct" Question?

Phrases synonymous with "you're welcome" may include "I was glad to do it," "no thanks needed," "don't mention it," or "no problem," depending on why the person is being thanked. Notice how all of these are written. In this case, the idea of "welcome" is a gesture of gladness, and does not directly refer to "welcome" as a noun or verb (such as "warmly welcoming" someone, or "giving a warm welcome"). Think of it as a shortened version of "you are welcome" to... whatever was just done.

To say "you're welcomed" would imply that the term was used in the active sense (as a verb, like in "you are welcomed by us all"). Although this is grammatically correct (particularly in that other sense), it is clumsy, a bit archaic, and not a traditionally acceptable answer to "thank you."

welcome- ninth meaning in dictionary.com is " without obligation for a favor received"

Therefore, I would think "You're welcome" is correct because it basically means "you are without obligation" or "I accept your gratitude."