The US firm announced that it had flown the 737 Max with the updated software on 207 flights.
It added it would provide data to the Federal Aviation Administration (FAA) on how pilots interact with controls and displays in different scenarios.
The FAA expects Boeing to submit the upgrade for certification next week.
An Ethiopian Airlines flight crashed in March, killing all 157 people on board.
It followed the Lion Air disaster in Indonesia in October, in which 189 people died.
Both crashes were linked to the Boeing 737 Max’s Manoeuvring Characteristics Augmentation System – a new feature on the aircraft which was designed to improve the handling of the plane and to stop it pitching up at too high an angle. Boeing said that once information on how pilots work with the upgraded system is submitted to the FAA, it will work with the regulator to schedule a certification test flight and submit final certification documentation.The company also said it had completed associated…