Council members are expected to advertise the opening and meet with applicants before a final vote. Republicans hold a 4-3 majority on the council. There is no rule preventing Walker or Grasso from voting for themselves.
Hammond, the county's chief administrative officer, has said he would continue as acting executive for as long as the council would have him, but that he would not run for the job in 2014.
Leopold signed an executive order Monday designating Hammond acting county executive "in the event of my temporary disability or absence from the County." Sweeney delivered his verdict Tuesday and the executive was suspended.
Leopold's resignation letter was dated Thursday. He wrote that his resignation would take effect Friday.
"It was a compelling and humbling experience for me to sit through two weeks of the trial and listen intently to the words expressed by the Court," Leopold wrote. "I acknowledge the serious errors in judgment that I made and do not want these errors in judgment to further distract the County from its ability to move forward in a positive way."
Baltimore Sun reporter Erin Cox contributed to this article.