The agreement calls for Williams to withdraw from the race in which she is the sole candidate for the seat held by Judge James Osborne, the Daily Report reported.
Osborne also would be unable to seek re-election or reappointment to the post he has held since 2005, the newspaper reported.
The agency, which has the power to remove a judge for ethics violations, is agreeing not to pursue ethics charges against Osborne or Williams, though she could seek another judicial position in the future, the paper reported.
If Williams withdraws, the Secretary of State would call a special election for the Paulding judgeship and set dates for qualifying, according to a source.
The action comes after a Georgia government watchdog group on Thursday asked Williams to withdraw from the election, calling her method of qualifying "neither honest, ethical" or bringing "integrity to the electoral process."
Williams qualified March 7 for the judgeship after Osborne qualifed for re-election March 3. Osborne then formally withdrew from the race Monday, leaving his daughter the only candidate.
Common Cause Georgia director William Perry asked Williams in the letter to also withdraw from the race.
"We believe your actions concerning your qualification as a candidate for the position of judge of the Superior Court of the Paulding Judicial Circuit, in which you admit that you and your father colluded to give yourself “the best opportunity to serve in the position” as reported by the [Atlanta newspaper] Daily Report is neither honest, ethical or brings integrity to the electoral process.
"You and your father’s actions, which included your father qualifying as the incumbent judge knowing he would withdraw his qualification, coupled with you qualifying in the closing hours of the qualifying period knowing you would be the only candidate remaining on the ballot, is unfair to the voters of Paulding County.
"Furthermore, this is not only unfair to the voters, but also to other potential candidates who may well have qualified had they known that they would not face an incumbent judge in the election."
By withdrawing, "you will allow the citizens of Paulding County to have a true choice in an honest, open, fair electoral process," the letter states.
"Common Cause Georgia will not object to you resubmitting your candidacy and qualifying in this second qualifying period because we truly believe that the voters of Paulding County should have the opportunity to choose their candidate. Should that candidate be you after a fair election, then we will congratulate you on the well deserved honor."