The firm said it had inadvertently made an alarm feature optional instead of standard, but insisted that this did not jeopardise flight safety.
All 737 Max planes were grounded in March after an Ethiopian Airlines flight crashed, killing 157 people.
Five months earlier, 189 people were killed in a Lion Air crash.
The worldwide fleet of 737 Max planes totalled 387 aircraft at the time of the grounding.
The feature at issue is known as the Angle of Attack (AOA) Disagree alert and was designed to let pilots know when two different sensors were reporting conflicting data.
The planemaker said it had intended to provide the feature as standard, but did not realise until deliveries had begun that it was only available if airlines purchased an optional indicator.
It said it had intended to deal with the problem in a later software update.
Boeing maintained that the software problem "did not adversely impact airplane safety or operation".
The US Federal Aviation Administration told Reuters news agency that Boeing had not informed it of the software issue until November 2018, a month after the Lion Air crash.
The FAA said the issue was "low risk", but said Boeing could have helped to "eliminate possible confusion" by letting it know earlier.
The flight angle of the plane has been identified as a factor in the disasters. Boeing has said that in both fatal crashes, erroneous AOA data was fed to the jet's Manoeuvring Characteristics Augmentation System (MCAS), an anti-stall system which has come under scrutiny since the crashes.
Boeing is developing new software for MCAS.