The Eagle Mine is expected to start production in the fourth quarter of 2014, with output targeted at some 23,000 metric tons of nickel and 20,000 metric tons of copper annually over the first three years of full production.
Rio Tinto, with $19 billion of debt, has vowed to slash costs and divest non-core assets.
The Michigan project is set to be Lundin's first mine in North America. It will pay $250 million for the half-finished project, and spend $75 million in construction costs before closing the deal.
Lundin said it expects cash costs to average about $2 per pound of nickel in the first three years.
The deal, which is subject to regulatory approvals, is expected to be completed in July 2013.
Reporting by Julie Gordon and Allison Martell; Editing by Richard Chang