Make somebody’s acquaintance
Definition 1 of 1
Pro Tip 1/3Polite Introduction
Used in polite or formal situations when meeting someone new, implying respect and a desire to know them. 
It's a pleasure to make your acquaintance, Professor Higgins.
Pro Tip 2/3First Encounter
Emphasizes the first time you meet someone. It isn't used for someone you've met before. 
Upon entering the meeting room, I was delighted to make your acquaintance.
Pro Tip 3/3Slightly Formal
Though polite, the phrase can come off as slightly formal or old-fashioned in casual settings. 
I'm Noah, and I'm thrilled to make your acquaintance.