The group is expected to take delivery of the £2.1 billion order in stages in the period to 2022.
Its supervisory board approved the investment during a meeting on Monday (May 7).
The order includes two Boeing 777-300ER long-haul aircraft for SWISS, which will supplement its fleet from early 2020 and expand its route network.
Two Boeing 777F, meanwhile, will replace Lufthansa Cargo’s MD11 aircraft, reducing fuel consumption, noise and costs.
Lufthansa said its expansion and modernisation plans came amid first quarter profit margins of more than 9% for SWISS and more than 10% for Lufthansa Cargo, its best for a decade.
