While both sentences (and your translations into English) are correct, so is your feeling of the first(corrected after comment) sounding weird.
Whether you are a native German speaker or, most probably, learning German from the background of an native English speaker, the first example example
Das wird bis Freitag fertig gewesen sein.
is highly uncommon in colloquial and spoken German, and quite rare in written context, which explains your feeling of weirdness about it. A lot of native speakers won't even be able to identify the tense correctly, especially if used in combination with Konjunktiv or subordinate clauses.
What we are looking at is the following construction:
- conjugated form of werden in Präsens which in this case is "wird"
- Partizip II of the actual verb, in this case "sein", which is "gewesen"
- infinitive form "sein" or "haben", depending on correct use with the Partizip II
This tense is called Futur II. It expresses an estimation, that an action has been completed at some future time, which in my opinion and contrary to the opinion of @Janka gives enough reason to call it Futur II. From my experience, native German speakers tend to underuse some tenses while also using others wrongly. This causes quite a dilution. For example, in spoken German the Präteritum is very rare, as it is mostly replaced by use of Perfekt. Most often, a future-directed action is told in Präsens like
Ich gehe Eis essen. Kommst du auch mit?
I'm going to get some ice cream. Do you want to come along?
(where the speaker had better said)
Ich werde Eis essen gehen. Wirst/Möchtest du auch mitkommen?
Even to me the second variant sound like distant future, so there seems no practical need to think of a tense for expressing future completed actions.
The example you chose is especially puzzling in its construction, because the main verb "fertig sein" has two parts and is based on the irregular conjugation of "sein". Please let me give you some more sentences to illustrate this:
Ich werde etwas morgen erledigen. (Futur I)
I will get something done tomorrow.
Ich werde etwas morgen erledigt haben. (Futur II)
I will have gotten something done tommorow.
The Futur I case expresses the subject's determination to start the action tomorrow, while the Futur II case expresses the subject's determination to finish the sction by tomorrow.
To me, the concept and relation of Futur I and Futur II is like the relation between Präsens and Perfekt and between Präteritum and Plusquamperfekt.
This opinion stems from a Latin background, where the relation is even more emphasized by the composition of the conjugated form. See e.g. this source.