All teams have selected an independent neurologist and they have been approved by the league.
Dr. Kenneth Perrine, a neuropsychologist at Hackensack University Medical Center in Hackensack, N.J., told MedPage Today that he thought the new policy would have a positive effect around the league.
"I think it's going to encourage the players to go through the process," said Perrine, who is the consulting neuropsychologist for the NFL's N.Y. Jets and the National Hockey League's N.Y. Islanders.
But, he added, "we've been pretty cautious anyway." According to Perrine, many of the newly mandated rules are already in place, at least in his experience.
The only aspect of the policy that is actually new, he said, is the requirement for teams to have an independent neurologist.
In the memo announcing the policy, Goodell urged players to be forthcoming about their condition.
A survey conducted by the Associated Press last month found that 30 of 160 NFL players had hidden or downplayed the effects of a concussion at some point during their careers, likely because of both a fear of letting down their team and a culture in which players are expected to play through pain.
But Perrine said players have become more aware of the seriousness of concussions in recent years and have become more candid about feeling ill effects.
"They realize that this is their profession, this is their game, but it's also their lives, and they want to make sure that they're not going to do something that's going to have a negative impact down the line," he said.
Wright said only time will tell whether the new policy does enough to protect players' health.
"The only way to tell if it goes far enough is to track the health of the players over the coming years and to make sure that there's a demonstrable improvement in their health long term, that we're not seeing the types of memory problems, the types of health problems that we've seen in the past," she said.
Associated Press reports contributed to this report.