TOKYO—Nissan Motor Co. on Thursday completed its purchase of a controlling stake in scandal-hit Mitsubishi Motors Corp. for more than $2 billion, a deal aimed at boosting scale to take on the world’s top auto makers.

With the addition of Mitsubishi, the 17-year-old alliance between Nissan and Renault SA produces around 10 million vehicles a year, making it one of the three largest automotive groups in the world, behind Toyota Motor Corp. and Volkswagen AG, said Carlos Ghosn, chief executive of both Renault SA and Nissan.

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