Luke Hall told a Commons debate that the functions of the Police and Crime Commissioner (PCC) will transfer to the mayor as part of West Yorkshire's £1.8 devolution deal.
Current West Yorkshire crime commissioner Mark Burns-Williamson has the power to set West Yorkshire Police's budget and its priorities as well as hiring and firing the Chief Constable.
Not all metro mayors take on these powers though in Greater Manchester the role is held by Andy Burnham's appointed deputy, former MP Beverley Hughes.
And during the Commons debate a Tory MP criticised the mayor's office over a scandal at Greater Manchester Police which saw the force fail to record about 80,000 crimes in a year and close cases without proper investigation.
It comes amid reports that Boris Johnson has resolved that the English local elections scheduled for May 6 should go ahead as planned, despite fears they may have to be postponed due to the pandemic.
The elections, including those for police and crime commissioner, were due to be held last May but postponed until this year.
West Yorkshire officials had originally planned for the new mayor to not take on the police and crime commissioner's powers until 2024 so that it would coincide with the end of the metro mayor's first-three year term.
But they have since decided to move this forward by three years, partly to avoid accusations of wasting tax-payers' money by holding an unnecessary PCC election in West Yorkshire when the post would be abolished within three years.
It is expected that a deputy mayor for policing and crime will be appointed by whoever is elected mayor. Batley & Spen MP Tracy Brabin is the strong favourite after being named as Labour's candidate in December.
This week the latest stage of the legislation needed to create the new powers for the mayor was debated in Parliament. As part of the devolution deal signed last March they will get £1.8bn in extra funding over 30 years as well as powers over areas including housing, education and transport.
Local Government Minister Luke Hall said that as part of the transfer of powers a new police and crime panel would be created to scrutinise the deputy mayor.
But the process was criticised by Conservative MP William Wragg, who said the Government risked a "hangover" from the days of former Chancellor George Osborne. Mr Osborne's Northern Powerhouse speech in 2014 was what led to the creation of most of the metro mayors in place today.
Mr Wragg said: "A number of us felt that we had dismissed the legacy of the ancien régime in our party, but we seem to be making exactly the same mistakes again.
"I draw to the Committee’s attention the recent issues in Greater Manchester, in particular the combination of the police and crime commissioner role with that of the Mayor, and the complete lack of accountability for what has been a tragedy for 80,000 victims of crime who were unable to register those crimes.
"I mention that because, as we amalgamate and create new structures, we are in danger of forgetting what powers of scrutiny there may be.
"A cursory glance at the draft order shows that the Mayor has the ability to appoint deputies who are themselves entirely unaccountable to the electorate."