The current airport, which is only able to handle limited daytime flights, was not sufficient, Ollanta Humala said.
The government will invest $460 million in the project, he said.
Machu Picchu is Peru’s top tourist attraction but there are concerns over the impact of high visitor numbers.
“This new airport will not only mean more tourists will be able to come, but it will generate more jobs… and help surrounding communities,” President Ollanta Humala said.
At a ceremony on Wednesday, he enacted a law that allows the expropriation of land in the town of Chinchero where the new international airport would be built.
The investment would help the government to tackle poverty, he said, “while always respecting ancient culture”.
Tourism is the main source of income in the region.
Machu Picchu is a world heritage site and the UN’s cultural agency, UNESCO, has previously warned about uncontrolled access and urged the authorities to make conservation a priority.
Currently, entrance to Machu Picchu is limited to some 2,500 visitors a day, amid concerns about the impact on the environment and citadel.
Cusco is the main starting point for visitors wishing to visit the site, who can make the 112 km (70 mile) journey either on foot or via bus and train.
The citadel of Machu Picchu, located 2,500 m (8,200 ft) above sea level, was built in the 15th Century by the Incas.
It was rediscovered in 1911 by US historian Hiram Bingham.
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