"Hierbij geef ik het woord aan de directeur."
Translation:I am hereby giving the floor to the director.
It is a different idiomatic expression in either language. In english yo give the floor to someone, in dutch it is the word.
It's an idiomatic expression. "Geven het woord" is like "to yield the floor." It's giving way to another speaker (to occupy the floor or to to say a word). More casually, one might say "to hand over the mic (microphone)."
For those who couldn't immediately figure out the context of this sentence (like me), it uses the compound verb "het woord geven" which means calling someone up (e.g onto the stage) to give a speech after an introduction.
"I hereby give" (or even "I am hereby giving", but not as much so) is much more natural sounding English than "Hereby I am giving". Probably because of the awkward double 'i' sound with "Hereby I".
If possible, I'd recommend you change the suggested translation.
Not that archaic though, but rather formal. And I always use it along with thereby, henceforth, thence etc.. for my essays. Plus I sometimes use it in regular conversations.