Those conditions include the company's share price outperforming a comparison index made up of a 50-50 mix of the NZX All Index and the Bloomberg World Airline index over a three year period.
Half of the rights will convert to shares if the share price matches the index over the period and for each 1 per cent the share price beats the index a further 2.5 per cent of the rights will convert to shares until the maximum of 100 per cent has been reached.
At the most recent share price of $2.82 the rights are worth around $1.95 million to Luxon.
Across the 11 people the rights were issued to the total worth could be worth as much as $13.4 million.
Luxon already owns 4,303,414 shares in Air New Zealand worth $12.14 million at the current share price.
The 49-year-old spent eight years at the company and nearly seven as chief executive.
He will now pursue a career in politics after announcing he will stand in the Botany seat in Auckland for the National party at next year's general election.
Air New Zealand chief financial officer Jeff McDowall is currently the acting chief executive and will hold the fort until new CEO Greg Foran, a Kiwi who has been working as a top-level boss at Walmart takes on the top job.