Common ways to offer a chair to someone entering your desk are :

Je vous en prie / Je t’en prie (while pointing the chair with your hand)

is quite formal, just as “Veuillez” would be.

Je vous en prie, asseyez-vous / Je t’en prie, assied-toi

It is quite the same as the first suggestion, but with no ambiguity on what you are talking about.

Asseyez-vous / Assieds-toi

Here, you want the person to sit, the tone defines if it is an order or a suggestion.

Vous pouvez vous asseoir / Tu peux t’asseoir

Here, the person was waiting for a chair, it is use in a classroom for example, when the teacher is coming in. Where the person didn’t have the right to sit, and you are giving him the right.

I will add additional info to Random’s reply.

• To a friend, (most) family members

Assieds-toi (s’il te plait)

• Same in plural. Also work with unknown people but in this case, you should really say “s’il vous plait”, otherwise it will sound aggressive.

Asseyez-vous (s’il vous plait)

• To an unknown person older than you (or your age if you want to be respectful)

  As far as I know, it can be misunderstood by people in Switzerland where they will just understand that they can sit but they won’t do it. They just understand the possibility “they can”. However all people from France will understand that you are asking them to sit.

  Contrary to the first sentences, the following ways have a possibility of people refusing to sit (because they prefer to stand or whatever the reason can be).

Vous pouvez vous asseoir

• To an unknown person younger than you (or your age if you want to sound friendly)

Tu peux t’asseoir