Hi Kate, This should be "here you are". Perhaps you're thinking of the inversion that happens in sentences such as "here comes the doctor"? If this is the case, remember that we only use inversion in this way when something is moving toward or away from the speaker, or when talking about things that are going to happen soon (here comes lunch) or about things being lost (there goes $50) or about things ringing (there goes the phone). I hope this helps

For the situation you describe, "so there you are!" feels more natural to me than "here you are". I know that seems counter-intuitive because you are all together "here", not "there". But you have been looking for them in many places, and you have finally found the place where they are. Saying "there" puts you in a frame of reference where you are in another place still searching for them. But "here you are" is good too.