I am writing to let you know that we have completed our search, and that you are no longer under consideration.
There's really a couple different things you could say about this. One is, if they've just told me they completed their search, they don't need to tell me I am no longer under consideration. See, what "we have completed our search" means is that no one is under consideration any more, because all the consideration is over.
The other thing is the weird switch from active to passive in the middle of the sentence. It's like there's someone doing the action right up to the moment where things get awkward, and then they very discreetly bow out of the sentence to let events unfold without them.