The plane maker said in a statement on Thursday that it has flown the aircraft with the updated software on 207 flights for more than 360 hours, reports CNN.
The software heads next to the US Federal Aviation Administration (FAA) and its counterparts in other countries that want to review it.
"We're committed to providing the FAA and global regulators all the information they need, and to getting it right. We're making clear and steady progress and are confident that the 737 MAX with updated MCAS software will be one of the safest airplanes ever to fly," Boeing CEO Dennis Muilenburg said in the statement.
"Boeing has developed enhanced training and education materials that are now being reviewed with the FAA, global regulators and airline customers to support return-to-service and longer-term operations," the company statement said.
"This includes a series of regional customer conferences being conducted around the world."
An FAA spokesman however, said later Thursday that the Boeing materials, including the software, have not yet been submitted.
The development comes ahead of an international gathering of aviation regulators in Dallas next week to discuss the reviews of the MAX.
The 737 MAX 8 and 9 were grounded worldwide after the March 10 Ethiopian Airlines crash that investigators have described as appearing similar to a Lion Air accident that took place in Indonesia last October. A total of 346 people died in the two crashes.
In both accidents, the automated Maneuvering Characteristics Augmentation System, or MCAS, pushed the planes' noses down while the pilots struggled to regain control.
Multiple investigations, including the initial crash investigation, are ongoing.
Criminal prosecutors, Congressional staffers and the Transportation Department inspector general are reviewing the initial certification of the 737 and the FAA's processes.
Aviation regulators in other countries will complete their own reviews of the software separate from the international Joint Authorities Technical Review the FAA has organised.