Ryanair is ordering 100 firm aircraft and placing options on another 100, the carrier says. The jets will be fitted with 197 seats.
The airline will take delivery of the jets – branded as the ‘Max 200’ – from 2019 to 2024.
Ryanair had already disclosed it was holding talks over a possible Max agreement, following its order for 175 Boeing 737-800s last year.
The 737-800 has a maximum capacity of 189 seats and Ryanair had expressed strong interest in a 200-seat version of the re-engined Max 8.
Boeing revealed during the Farnborough air show in July that it would offer such an aircraft, through modifications to the exit-door arrangement.