Greg Dyke has invited Astle's widow Laraine and his daughters, Claire and Dawn, to Wembley Stadium on 10 August.
The ex-West Bromwich Albion and England forward died in 2002.
A neurosurgeon said last month that he died from a brain condition linked to boxers rather than Alzheimer's disease as previously thought.
Dawn Astle said: "We want to stress the immediate message in dealing with head injuries and concussions, to discuss the FA's medical policies on this and work on player education.
"[The issue] has to be taken seriously because it's about lives.
"It's not like a back or knee injury, because once the brain is damaged it doesn't repair itself and Dad is proof of that."
Ms Astle said Dr Willie Stewart, who carried out a new examination of Mr Astle's brain, would also be at the meeting.
Astle's family have campaigned for the FA to carry out research into the risks of heading footballs and players suffering concussion.
The Justice for Jeff group has also held protests at West Brom games.
The FA previously apologised to the family for not keeping them informed about its work and said its rules on concussion were due to be changed ahead of the 2014/15 season.
A spokesman for the FA said Mr Dyke "had been keen to meet the Astle family for a long time" to hear their concerns.
It was initially believed Astle died from Alzheimer's disease, but the coroner at his inquest ruled his brain had been damaged by heading heavy leather balls.
He played for West Bromwich Albion from 1964-1974 scoring 137 goals in 292 league appearances.
The family of the former footballer Jeff Astle is to meet the FA chairman next month to discuss head injuries in the game, as part of their campaign.