Turnbull told iTWire that he was moving to the United States to take up a role as director of operations at Puppet Labs, which provides services for the open source Puppet configuration management system.
He has been involved with the Puppet project for about three years, initially helping out with the documentation and getting more involved as time went on.
"(This) gives me the opportunity to combine my passion for open source with my career," he said. "Given the distance and logistics I don't feel it is appropriate or practical for me to retain the role."
John Ferlito from New South Wales, who was elected treasurer of the organisation earlier this year, will be taking over from Turnbull.
Ferlito's post will be filled by Tasmanian web developer Joshua Hesketh.
Turnbull served on the Linux Australia committee as an ordinary member in 2008. He was chief organiser of the mini-conferences for the 2008 LCA which was held in Melbourne.
"The handover was conducted in accordance with the Linux Australia constitution and I am sure John will do an excellent job in the role," Turnbull added.