The terms of the deal weren't disclosed.
The acquisition includes the advanced Honeymoon Well project, as well as a 50% interest in the Albion Downs North and Jericho exploration projects.
BHP already held the other 50% of Albion Downs North and Jericho.
The projects are about 50km from BHP's Mt Keith mine and 100km from its Leinster concentrator in the northern Goldfields.
The package includes the high-grade Wedgetail nickel sulphide deposit and a high-quality disseminated sulphide resource in the style of BHP's Mt Keith and Yakabindie orebodies.
In 2012, Norilsk envisaged Honeymoon Well as a 40,000 tonne per annum producer, based on a resource of 1.16 million tonnes of contained nickel.
Capital costs had previously been estimated at US$1.5 billion.
BHP Nickel West asset president Eddy Haegel said the acquisition represented an exciting opportunity to enhance its world-class nickel resource base in Western Australia.
"Proximity to our existing facilities makes us the natural owners of these deposits, and provides potential options to bring the undeveloped resources to market," he said.
"Nickel continues to be an essential input into new technologies that will improve the battery storage needed for renewables and electric vehicle manufacturing.
"Consistent with our strategy to invest in future facing commodities, this transaction gives us access to explore and develop these prospective nickel sulphide tenements."
The sale marks Norilsk's formal exit from Australia.
"With the sale of Honeymoon Well nickel project we complete the strategic exit from Australian operations and reinforce our focus on the development of our tier one asset portfolio in Russia," Norilsk senior vice president for strategy, strategic projects, logistics and procurement Sergey Dubovitsky said.
"We are grateful to BHP as our JV partner in Australia and appreciate their commitment to prompt execution of the transaction."