Porters, cleaners and security staff have voted to take industrial action over the Trust's plans to set up a new company to run the facilities.
It would mean members would no longer be employed by the NHS – described by three of Bradford’s MPs as “backdoor privatisation”.
Pickets lines are expected outside the Trust's hospitals, including Bradford Royal Infirmary and St Luke's hospital, from 6am.
Some 97 per cent of votes cast by members were in favour of strike action at a ballot in June.
Union UNISON said that the strike will affect staff right across the Trust.
The walkout is due to last seven days.
Other centres affected include Shipley Hospitals and three community hospitals at Eccleshill, West Wood Park and Westbourne Green.
UNISON Regional Organiser Natalie Ratcliffe said members were angry at the proposals because they would no longer be employed within the NHS.
The Trust say they will guarantee that the affected staff would retain their existing pay and conditions of service for 25 years.
Ms Ratcliffe said: “Our members see this as a promise that can be easily broken and 97 per cent of them made the very difficult decision vote to take strike action.
“We have urged the Trust to scrap the plans, or at least shelve them, as there is likely to be a General Election this year or next and the policy of establishing wholly-owned subsidiaries is likely to be dropped.
“Other Trusts in the UK have dropped or shelved their plans, but the Bradford Trust seems hell-bent on imposing this company on our members and they are sufficiently angry and worried about it to have decided to go on strike.”
Bradford Teaching Hospitals NHS Foundation Trust website states that arrangements have been made to ensure that patient safety and levels of care are not compromised by the action.
Essential services, such as emergency and urgent surgery, will continue as normal.
Patients are being told to attend routine clinics and appointments as normal unless notified otherwise.
The Trust website states: "There will be picket lines outside the entrances to the Trust’s hospitals and we expect that pickets will behave in a responsible way; they will not be allowed to obstruct or intimidate patients and visitors and you will be able to gain admission to all our hospitals as normal.
"Similarly patients and visitors coming into our hospitals, crossing picket lines will also be expected to behave respectfully and refrain from using threatening or abusive behaviour towards the pickets.
"Drivers coming into hospital premises on the days of the industrial action are asked to exercise extra due care and attention when approaching or driving past/through a picket line and should not drive in a manner which could put people at risk or cause injury."
"Bradford Teaching Hospitals NHS Foundation Trust is setting up a wholly owned subsidiary company (WOS) for our Estates, Facilities and Clinical Engineering services, which will be entirely owned by the Trust. The new company, Bradford Healthcare Facilities Management Ltd (BHFML), will operate from 1 October 2019.
"Every year the Trust has to deliver efficiency savings – about 4 per cent of turnover (roughly £16m) in the current year. The Trust must take all steps to protect frontline services and provide safe and effective patient care."