The United Network for Organ Sharing (U.N.O.S.) is also poised to release data about individual transplant centers for the first time, including the survival rates of their patients.
The changes represent a retreat for the network after more than a year of defending its current system under pressure from the Department of Health and Human Services.
HHS issued rules last year ordering the network to create a new system that would get more organs to the sickest patients. But the network has insisted on its system, which relies heavily on geography.
The HHS rules also called for the network to release more data, but transplant centers have balked, saying it was unfair to release potentially embarrassing or misleading data about individual hospitals and doctors.
Hoping to stop these rules, the network mounted an intense lobbying effort and persuaded Congress to delay them until the fall.
But, meeting Thursday in Atlanta, the board moved closer to what HHS wants.
In distributing donated organs, the liver policy has engendered the fiercest debate, partially because there is an acute shortage of livers and very few other medical options for patients who need new ones.
The policy adopted Thursday will direct more livers to the sickest patients, those classified as "status 1." These are people who are suddenly struck by liver disease and have a week or less to live.
Under the current system, livers are offered first to status 1 patients in the local area. If there are no medical matches, they are offered to other local patients, in order of medical urgency. If there are still no local matches, livers are offered to patients in the surrounding region, sickest first.
The new policy would kick in if there are no local status 1 matches. In this case, livers would be offered to status 1 patients throughout the region before being offered to less urgent local candidates.
"The sickest person in that status gets the first organ that is suitable for them in that entire region," Dr. Jeremiah Turcotte, chairman of the U.N.O.S. Liver Committee, told CBS News. "So that's a major sharing effort."
Under current policy, 9.7 percent of donated livers go to status 1 patients. The network expects that to rise to 14.3 percent under the new policy. The percentages going to less urgent patients - those in status 2A, 2B and 3 - all drop slightly.
The HHS regulation wanted the network to go further, although government officials have said they are willing to compromise. The rule called for the elimination of geographic boundaries, while the new network policy still relies on regional lines.
A liver donated in Cleveland, for instance, might be directed to someone who is relatively healthy even if there is a status 1 patient in nearby Pittsburgh, because the egional line is drawn between Pennsylvania and Ohio.
Nationally, there are 63 local areas and nine regions.