The Dallas-based carrier said the aircraft will increase its fleet's fuel efficiency as it retires older 737 models.
"Today's environment demands that we become more fuel-efficient and environmentally friendly, and as the launch Customer of the Boeing 737 MAX, we have accomplished both," said Southwest chief executive Gary Kelly in a statement.
Financial details of the transaction were not released and Boeing has not unveiled the price tag of a Boeing 737 MAX. Current 737 next-generation models, which include the Boeing 737-700, 737-800 and 737-900 cost around $80 million a piece.
Southwest announced it is also purchasing an additional 58 Boeing 737 next-generation models and has substituted Boeing 737-800 models for all of its existing Boeing 737-700 aircraft deliveries in 2012 and 2013.
With the new plane order, Southwest said it has a total of 350 aircraft on order from Boeing for 2012 through 2022. The company says it also has options to purchase 78 Boeing 737 next-generation model and 150 737 MAX, bringing its total option position between 2014 and 2027 to 242 aircraft.
Earlier this fall, Southwest said it planned to add 33 Boeing 737-800s next year while retiring a similar number of its 737 "classic" planes.
Boeing said the 737 MAX model will feature CFM International LEAP-1B engines and will be 16 percent more fuel-efficient than current competitor aircraft models. The re-engined 737 model will also have a larger range. The first flight of the 737 MAX is scheduled for 2016 with customers receiving the aircraft in 2017, two years after its competitor, Airbus, is scheduled to deliver its re-engined A320NEO aircraft to customers.
Southwest was also the launch customer for Boeing's 737-300, 737-500 and 737-700 models.
The Chicago-based aircraft manufacturer had recently announced it had ramped up production of its 737 aircraft to 35 a month to meet customer demand. Boeing added it plans to increase the rate to 38 airplanes a month by the second quarter of 2013 and then 42 airplanes a month in the first half of 2014.
Fort Worth-based American Airlines was the first carrier to commit to buying the re-engined version of the Boeing 737, announcing in July that it planned to buy 200 Boeing 737 series aircraft, half existing next-generation models and 100 re-engined aircraft.
The deliveries of those aircraft are scheduled between 2014 and 2022. However, with American's parent company, AMR Corp., filing for bankruptcy last month, it is unclear on what will happen with the large plane order. AMR management has said it intends to proceed with its 460-plane order from Airbus and Boeing as part of its restructuring plan.
A press conference is scheduled for 9 a.m. CST at Southwest's headquarters at Dallas Love Field. Follow @Sky_Talk for live tweets from the news conference.