Gill had previously refused to attend the same meeting as Sepp Blatter, in protest at his election for a fifth term as FIFA president.
The FA vice-chairman has agreed to attend an emergency meeting that will determine the date for an election to appoint Blatter???s successor.
Blatter announced last month that he intends to leave his position, and Gill will be part of the election decision-making process at FIFA headquarters in Zurich on July 20.
Sky Sports News HQ understands that Gill, who is also a UEFA Executive Committee member, made his decision because Blatter will leave his position.
UEFA has eight members on FIFA???s all-powerful committee, including president Michel Platini.
It is understood Gill has not changed his hostile stance on Blatter???s presidency, and the former Manchester United chief executive strongly criticised Blatter after FIFA???s annual congress in May.
Gill, who replaced Jim Boyce, said in a statement after Blatter???s re-election: ???The terribly damaging events of the last three days have convinced me it is not appropriate to be a member of the FIFA Executive Committee under the current leadership.
“My professional reputation is critical to me and I simply do not see how there will be change for the good of world football while Mr Blatter remains in post.???
Blatter responded: ???If you are elected you have to come, whoever is president of FIFA.?????