Two fatal 737 Max crashes killed 346 people within five months, in 2018 and 2019; one in Indonesia and the other in Ethiopia.
Following the crashes Boeing's best selling plane was grounded for 20 months, then returned to service after the company made significant software and training improvements.
The proposed agreement was filed to a Delaware court on Friday and confirmed by Boeing.
It requires that within one year an additional board director be elected who has experience in aviation, aerospace, engineering or product safety. And it calls for there to be at least three directors with safety-related experience.
The settlement must be approved by a judge to become final.
The lead plaintiffs, New York state comptroller Thomas P DiNapoli and the Fire and Police Pension Association of Colorado, said if approved the settlement would be the largest through the court on allegations directors failed to protect against the risk of harm.
Boeing's board "failed in their fiduciary responsibility to monitor safety and protect the company, its shareholders and its customers from unsafe business practices and admitted illegal conduct," DiNapoli said.
"It is our hope, moving forward, that the reforms agreed to in this settlement will help safeguard Boeing and the flying public against future tragedy, and begin to restore the company's reputation."
However in the settlement the current and former directors state they do not admit wrongdoing, and that they acted in the best interests of Boeing and its stockholders.
Under the settlement, Boeing will also create an ombudsman's program for at least five years so work-related concerns can be raised by its employees conducting aeroplane certification work for the Federal Aviation Administration.
Its chief executive and board chair position will be separated, and it must provide public reports on all safety enhancements since the Max air disasters.
The financial penalty will be paid by insurers to Boeing, apart from up to $29.7 million in legal fees and expenses to the shareholder attorneys, the documents showed.
The Delaware court earlier ruled Boeing stockholders could pursue some claims against the board. It said the first 737 Max crash was a "red flag" about a safety system known as MCAS "that the board should have heeded, but instead ignored."
The crashes cost Boeing about $20 billion.
The company agreed to a deferred prosecution agreement with the US Department of Justice in January, including $2.5 billion in fines and compensation stemming from the 737 Max crashes.
It confirmed the settlement and said since the crashes "Boeing has taken significant actions to reinforce and strengthen our commitment to aviation safety".
It added that the settlement "builds on those actions with additional oversight and governance reforms that will further advance safety and quality in the work that we do."
Boeing's board includes the recent additions of retired lieutenant general Stayce Harris, who has over 10,000 hours experience as a pilot of Boeing aircraft; and David Joyce, who led GE Aviation from 2009 to 2020.