The order consists of 25 Max 200s (currently used only by Ryanair) and 25 Max 10s (after certification).
Industry sources have suggested that Boeing has put together a favourable package for IAG in order to boost its order books after a dark period for the US airframer.
IAG said they had negotiated a substantial discount off the list prices.
The first aircraft will be delivered in 2023 and the order includes options for 100 more aircraft for delivery between 2025-2028.
Boeing has been in turmoil recently with the 737 Max requiring re-certification following two fatal crashes and delays plaguing its 787 and 777X deliveries.
Luis Gallego, IAG´s chief executive, said: “The addition of new Boeing 737s is an important part of IAG´s short-haul fleet renewal. These latest-generation aircraft are more fuel-efficient than those they will replace and in line with our commitment to achieving net-zero carbon emissions by 2050.”
Whilst the destination airliners haven’t been announced for the order, Spanish low-cost carrier Vueling is likely to be one recipient of the Max 200 variant.