I would call this a sentence adverb:
an adverb or adverbial phrase that expresses a writer's or speaker's attitude to the content of the sentence in which it occurs (such as frankly, obviously), or places the sentence in a particular context (such as technically, politically).
Usage note from About.com:
Unlike an ordinary adverb — which is conventionally defined as a word that modifies a verb, adjective, or other adverb — a sentence adverb modifies a sentence as a whole or a clause within a sentence.
Dozens of words can be used as sentence adverbs, among them actually, apparently, basically, briefly, certainly, clearly, conceivably, confidentially, curiously, evidently, fortunately, hopefully, however, ideally, incidentally, indeed, interestingly, ironically, naturally, predictably, presumably, regrettably, seriously, strangely, surprisingly, thankfully, theoretically, therefore, truthfully, ultimately, and wisely.
Well may well be used as a sentence adverb as well. Or it could be construed as an exclamation.