Gill, a Manchester United director, confirmed he did not attend Saturday's first executive committee meeting following Blatter's re-election to a fifth term in office, where he was due to sit as Britain's FIFA vice-president.
Blatter beat rival presidential candidate Prince Ali of Jordan despite the crisis which has seen seven FIFA officials arrested, 18 people indicted by US justice authorities, and a Swiss criminal investigation into 2018 and 2022 World Cup bidding.
Gill said in a statement to the Press Association: "This action is not something I take lightly but 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.
"I do recognise that Mr Blatter has been democratically elected and wish FIFA every success in tackling the many troubling issues it faces
However, 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.
"I will continue to focus on my positions within the FA and UEFA, which I take seriously and am privileged to hold."
The British vice-presidency is elected by UEFA members and an election for that post is now likely to take place.
Gill added: "As I explained to my European colleagues at the UEFA meeting on Thursday, I will not be taking my place on the FIFA executive committee
Out of respect for the FIFA Congress and the other 208 member associations, it was right to wait until after yesterday's election to confirm my decision."
Source : PA
Source: PA