Commissioner Roger Goodell will implement the policy as soon as details can be worked out. The neurologists will work with the teams' medical staffs.
Goodell recently urged players to tell their teams' medical staffs if they think a teammate shows symptoms of a concussion. He and union director DeMaurice Smith also testified before Congress at hearings on football head injuries.
The Associated Press this month conducted a survey of 160 NFL players - about 10 percent of the league - and 30 replied that they have hidden or played down the effects of a concussion.
Told of the AP's findings, NFL spokesman Greg Aiello said in an e-mail to the news agency that Goodell spoke to Smith about "the importance of players reporting head injuries, no matter how minor they believe they might be. The commissioner said that process needs to include players observing and reporting to the team medical staff when a teammate shows symptoms of a concussion."
The NFLPA said it opposes Goodell's suggestion that players tell medical staffs about possible head injuries to teammates.
"The players want a uniform standard for clearance to return to play that is at the current state of medical knowledge," NFLPA assistant executive director George Atallah told the AP in an e-mail Sunday. "It should not vary from team to team.
"Equally important, the NFL should release all aggregate medical data it collects from players every year. ... Our players are not test subjects."
The new NFL policy was first reported Sunday by Fox. The union wants the league to provide all information from researchers to the players, as well, believing such data could help retired players and youth players.
"We will continue to push the envelope on player safety," Atallah said, "and are happy when the NFL does as well."