Mr Woodall was elected as a City of Melville councillor in 2015, and served a term as deputy mayor.
He has worked as a commercial lawyer.
The Liberal Party WA announced the result on Twitter on Wednesday night.
Mr Nalder announced his retirement as member just weeks ago following an unsuccessful tilt at the party’s state leadership.
Bateman is seen as a safe Liberal seat for the state election due in March.
Mr Woodall was in a field of six candidates.
Mr Taylor had served a term as member for Bateman District from 2013 to 2017, but lost a preselection for the seat when it was redistributed to include large parts of Alfred Cove District, Mr Nalder’s former seat.
He then contested Bicton District in 2017, but the election that year was a wipeout loss for the WA Liberals.
Mr Taylor went on to lead the Western Rock Lobster Council, where he successfully fought sweeping changes proposed by the Labor state government.
Ms McSweeney has been principal of The PR Counsel for nearly six years.
She previously served as an advisor to Tony Abbott, and as a journalist with 6PR.
Local lawyer Anthony Jarvis, recruitment consultant Pierette Kelly, and former Australian Medical Association WA communications director and journalist Rob Reid were also in the field.