The government said that it was paying nearly $50 million to be shared among around 7,400 former employees of Mexicana de Aviacion, which collapsed in 2010.
An additional $235 million will be invested in the business, which will have a fleet of 10 leased Boeing 737-800 aircraft, it said.
The airline, which will be operated by the military-controlled group Olmeca-Maya-Mexica, will offer flights to destinations including the beach resorts of Cancun and Los Cabos.
Its main base will be Mexico City's second international airport, Felipe Angeles, built at a military air base north of the capital.
One of Lopez Obrador's flagship projects, it has struggled to attract airlines away from the city's main air hub, Benito Juarez, since opening in March last year.
The new carrier will offer tickets that are around 18 percent cheaper than those sold by rivals such as Aeromexico, Volaris and Viva Aerobus, according to the government.
"There's no desire for profit," Lopez Obrador said.
"All the works that we have done in this government have been done with a public budget and are works of the nation," he added.
Since taking office in 2018, Lopez Obrador has given increased responsibility to the armed forces, in addition to their public security role, including control of ports and customs and major infrastructure projects.
Earlier this year Aeromar, a small Mexican airline, closed due to financial problems.
jg-dr/tjj
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