The 100 airplanes are valued at USD 11 billion at current list prices, but buyers often get steep discounts off list prices for multiple passenger jets.
Ryanair initially had a commitment for the order in September.
The 737 MAX 200 is considered more fuel-efficient than most other current single-aisle airplanes and can accommodate up to 200 seats.
Ryanair's order includes options for an additional 100 737 MAX 200 aircraft.
Ryanair said that the order will increase its fleet to about 520 aircraft by 2024. The company runs more than 1,600 flights daily and now operates the biggest fleet of Boeing airplanes in Europe.