CEA's decision to transfer its order marks Boeing's ninth lost order since the beginning of the year.
CEA had previously revealed the plan to switch to the smaller 737s due to the delay in the delivery of Dreamliner aircraft and the slowing of demand for long-haul international travel.
Boeing spokesman Doug Alder was quoted by Bloomberg as saying this has been in the works for some time.
"It was just waiting for Chinese government approval," Alder adds.
The Dreamliner aircraft was three years behind schedule during its delivery to its first customer in September last year following problems with new production methods and materials.
Boeing has not delivered any 787 aircraft in February after it was forced to perform inspections on a manufacturing error of fuselage lamination.
The aircraft maker has recently received an order for two Dreamliners from Air New Zealand, but has reduced its net 737 orders by two following an undisclosed customer's cancellation of the order.
Boeing has received orders for more than 800 Dreamliners, while the current deal increases the aircraft maker's commercial planes order to 406 for this year.
Boeing 737 family aircraft are powered by the new CFM56-7BE engine, featuring Blended Winglets, which enhance its range, fuel efficiency and take-off performance while reducing carbon emissions, engine maintenance costs and noise.
Its flight deck features technologies including vertical situation display, which displays the current and projected flight path of the airplane and specifies potential conflicts with terrain and Head-Up Display, which facilitates pilots with eye-level flight and safety information.