Where Does Hopefully Come from?

From hopeful +‎ -ly. (Cf. German hoffentlich it is to be hoped.)

Is hopefully correct English?

Hopefully means “in a hopeful manner.” We looked hopefully to the future. Some usage experts object to the use of hopefully as a sentence adverb, apparently on grounds of clarity. To be safe, avoid using hopefully in sentences such as the following: Hopefully, your son will recover soon.

Why is hopefully wrong?

Hopefully is an adverb which means what it ought to [italics mine]–“full of hope” or “characterized by hope.” It normally modifies verbs. Nonstandard English sometimes substitutes the word hopefully for I hope (or some other subject with the verb hope). Incorrect: Hopefully, they will come in time.