If the context is clear, I think a good way to express what I think you mean (*) could consist of using the phrasal wave somebody over. Here follow a couple of examples taken from Google books:
Chad knew the moment he stepped into El Rosal for dinner that night he was in trouble. He thought he'd come in early -- just after five -- and would beat the Saturday crowd. The place was packed. No tables were free. No bar stool was empty. And there was a thrity minute wait for a table. The early-bird specials were apparently quite popular.
"Chad! Chad!" The mayor waved him over to a small table near the kitchen door. [...]
Who waved him over to join his table? Stan Musial, who was eating with Bob Gibson, Lou Brock and Jack Buck. It was apparently a very enjoyable lunch.
(*) Please notice, JJJJ, that "greet" means "say hi" and "wave" means "raise your arm and move your hand from side to side in order to make someone notice you". Even if we sometimes greet and make this gesture at the same time (see picture from the Longman dictionary below) and waving can be a form of greeting (see this article: https://www.theguardian.com/society/2018/apr/14/dad-wave-nod-how-greet-hug-kiss-handshake), they are not synonyms. However, as a teacher I understood what you meant.