Kelty joined the electric automaker in 2006, establishing himself as one of the company's longest-serving executives.
At Tesla, Kelty served as the head negotiator with Panasonic where he previously worked. Panasonic (PCRFY) is Tesla's partner in the Nevada gigafactory for battery production.
Kelty's departure comes just after Tesla rolled out its first Model 3 models to employees Friday night.
Shares of Tesla were sinking over 1.4% during afternoon trading on Thursday.
More of What's Trending on TheStreet: