A slightly modified version, the Personal Martin Jetpack, would be released in 2015 and "transform the future of personal flight", the firm said.
The company's website says prospective commercial customers can now place orders for the jet pack.
Coker joined the Royal Air Force in 1976 and amassed 5500 flying hours on 20 different types of aircraft, the Martin Aircraft Company said.
After leaving the RAF he emigrated to New Zealand and formed his own aviation consultancy business.
In his most recent role, Coker was general manager of Lockheed Martin Global Inc (New Zealand).
Coker said he had been a long-time observer of the Martin Jetpack and his decision to join the company was spurred by the "spectacular leap forward" in the aircraft's technological capabilities.
"I'm really excited to be leading this company forward and I have no doubt that, in the near future, the Martin Jetpack will be in use throughout the world," Coker said.
A Martin Aircraft Company spokeswoman said the firm's former chief executive, Richard Lauder, left the company in July 2012 to take up a role with a tourism operator.