Smith also shared the shot, with the caption: "Finally".
Goebel has become one of choreography's biggest names over the past decade, working with the likes of Jennifer Lopez, Justin Bieber, Rihanna, Janet Jackson, Niicki Minaj, Sir Elton John and Ciara.
In recent times Smith has also been a regular visitor to New Zealand.
He performed here last November, then returned two months later for a summer holiday, posting a picture of on arrival with the caption: "finally arrived in heaven".
Earlier this year Smith had a global hit with Dancing With a Stranger; his collaboration with American singer Normani. The official video for the track has been viewed more than 360 million times on YouTube.
Given the pictures Goebel and Smith have shared of each other hanging out, it appears the pair are anything but strangers to themselves.