West Lake Hills Mayor Linda Anthony said Vaughan resigned in order to run for the mayor's seat in the May election.
Anthony recommended the temporary appointment of former council member Jim O'Connor, who will fill the seat until a new member is appointed after the election. Council approved of the recommendation unanimously.
O'Connor has no interest in running for the open seat in the upcoming election, Anthony said.
With the resignation, the council also approved a special election to be held in May to fill the vacant seat.
City Council also adopted an ordinance calling for the May 4 general election to elect mayor, council member Place 2 and council member Place 4.
Anthony said the special election and general election will be on the same ballot.
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"My recommendation, in order to ensure smooth running of the council and the city ... and to avoid any possible hurt feelings or feelings that we had bias or favoritism in an appointment of somebody who might be considering running for the open seat, is that we look no further than Jim O'Connor," Anthony said.