Former Chief Constable Dee Collins retired from the force at the end of April due to health challenges following a career spanning three decades.
The force advertised the role on its website with a salary of £181,560.
Mr Burns-Williamson said he was looking for a "dynamic and forward thinking" chief police officer who can work with him and key partners to deliver police and partnership working, in alignment with his West Yorkshire Police and Crime Plane.
The PCC has now announced John Robins QPM as his preferred choice for the position of Chief Constable with the West Yorkshire force following interviews earlier this week.
Mr Robins has been Temporary Chief Constable since December 2018 and has worked for West Yorkshire Police since 1990.
He joined the force as a police constable before working his way up to Chief Superintendent, before becoming an Assistant Chief Constable and then Deputy Chief Constable.
Mr Burns-Williamson said: “I am really pleased to be making this announcement that John will be my preferred candidate, subject to a confirmation hearing with the West Yorkshire Police and Crime Panel in July where I will look forward to making this recommendation to the Panel members.”
Mr Robins said: “I am extremely proud and honoured to be the preferred candidate to be the next Chief Constable of West Yorkshire Police. My enthusiasm for policing and for West Yorkshire is as keen today as it was on the first day I joined.”