All 737 MAX planes have been banned from flying since March after crashes in Ethiopia and Indonesia that together killed 346 people in a space of five months.
A $50m (£40.2m) financial assistance fund was announced in July and will now be open to claims from family members.
The bereaved family members will not be required to give up their right to sue if they opt to claim money from the fund.
“We continue to extend our deepest sympathies to the families and loved ones of all those on board,” said Boeing CEO Dennis Muilenburg in a statement.
“The opening of this fund is an important step in our efforts to help affected families.”
Boeing said it assumes the 737 MAX will return to service in the US and other countries in the autumn but could not give an exact date.
However, last week Federal Aviation Administration chief Steve Dickson said Boeing was not yet ready to return the 737 MAX to service, with steps including submitting a pre-production version of a software update yet to be completed.
The 737 MAX began flying passengers in 2017 and is Boeing’s best selling aircraft. Despite this, less than 400 have been delivered to airlines.
In July, Boeing said there would be a $4.9bn (£3.9bn) charge to compensate airlines following the prolonged grounding of the 737 MAX.
In October 2018, a MAX aircraft operated by Indonesia’s Lion Air crashed, killing all 189 people on board.
A second crash happened in March this year in Ethiopia, killing 157 people, forcing regulators around the world to ground the plane.
A problem with the aircraft’s flight control software was initially identified as the cause, but later Boeing said further software problems had been found requiring further work.