Musk travelled to Jamestown, in South Australia's mid-north, on Friday where construction of the 100-megawatt battery is well advanced.
Introducing Elon Musk, a triumphant Weatherill said those who had joked about SA's fragile power system "are laughing out of the other side of their faces now."
A contract has been signed with electricity supplier Electranet. A Tesla spokeswoman said last night that the Australian Energy Market Operator had approved the "interconnection agreement".
She said Tesla and Neoen now had 100 days to complete the largest lithium-ion battery storage project in the world. She said it would provide enough power for more than 30,000 homes. "It will help solve power outages," she said.
Earlier this year the tech billionaire, 46, weighed into the state's energy crisis, boldly claiming he could fix the problem for AU$33 million (NZ$36m) and in under 100 days or it's free.
The battery systems will be paired with 99 wind turbines at Neoen's Hornsdale Wind Farm. Musk, greeted by the crowd with cheers and an "onya Elon", told guests the battery packs now on site had been installed within two months.
"You couldn't get your kitchen done that fast," he said.
The SA battery will bring added reliability and stability to the state's power supplies. It is thought to be costing taxpayers about AU$50m (NZ$54m) and forms part of the state government's AU$550m (NZ$601m) energy plan.
Other elements of the energy plan include installing emergency generators at two sites in Adelaide, a push for more gas-fired power generation and a solar- thermal power plant near Port Augusta.
It was prompted by a series of power issues, including a statewide blackout when a freak storm brought down transmission lines a year ago and another event last summer when heavy demand and a lack of electricity flowing through the interconnector with Victoria cut services to thousands of properties.