Super Mario Run will be released in Apple's App Store on 15 December, with users having to pay $10 (£8) for the full game.
Nintendo, which announced the tie-up last month, saw its shares jump by as much as 5%.
It hopes to build on the global success of its Pokemon Go app from earlier this year.
But because Pokemon was free to download, analysts said it did not generate as much money for the firm as it could have done.
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Smartphones are the gaming industry's fastest growing source of revenue and the Japanese firm has been criticised for being slow on the uptake.
It has promised to to unveil more gaming titles by March 2017, with an Android version of Super Mario Run also planned.
Shares in Nintendo have climbed after it announced a launch date for its new Super Mario game for the iPhone.