I have lived my whole life as of yet in Seoul.
Is this sentence correct?
Since you've already indicated that the duration is your "whole life," it is redundant to also add "as of yet." "I have lived my whole life in Seoul" would be sufficient and preferable. A more common word order would be "I have lived in Seoul (for) my whole life." Many would insert the word "for" since it usually used in contexts indicating duration. If you had lived there 10 years, you would say "for 10 years," for example. I don't think the "for" would actually be required, though.
An even simpler way to convey the idea would be to say "I've always lived in Seoul." In this context "always" just means "for my whole life," and not eternally, of course.
If you wanted to convey the idea that a change was imminent, or likely, you might say "To date," or "Up until now," I've always lived in Seoul. It wouldn't be redundant in that case, because you're actually adding something of significance.