This usage is perfectly grammatical and is explained in this article by Jakub Marian, but it is formal.
Just like “thus”, “hence” is an adverb, not a conjunction, so it cannot join two independent clauses (note that it is more common to omit the commas around “hence” than after “thus” in formal writing):
• He is not satisfied. Hence(,) we must prepare a new proposal.
• He is not satisfied; hence(,) we must prepare a new proposal.
• He is not satisfied, hence we must prepare a new proposal.
“Hence” used in this sense is rather uncommon, and such usage persists mostly in specialized fields, such as scientific writing.
There is, however, another, more common meaning of “hence”, which substitutes a verb but is not a clause in itself and is always separated from the rest of the sentence by a comma:
• Our server was down, hence the delay in responding.
• The chemicals cause the rain to become acidic, hence the term “acid rain”.
As you can see, “hence” substitutes phrases such as “which leads to” or “which is the reason of”.
"Thus" is another word such as "hence"; it can be used synonymously, in fact.
• His mother was an Italian, thus his name, Luca.
(ref.) From the beginning of his career as a Foreign Service professional he had felt himself entirely at home but also an alien in an irrelevant order, thus his threats to resign and his desire to plunge into the study of Chekhov.