BSW Group said the changes would create a single staffing service across the three trusts.
A spokesperson said the new arrangements would allow workers to access a wider range of shifts across multiple locations and make booking work “more streamlined and accessible”.
They added that “full financial due diligence” carried out before the contract was awarded.
The group said the changes would help increase staffing fill rates and support patient care.
It said that said most bank workers also held permanent NHS contracts and would continue to receive NHS pension benefits through those roles.
The spokesperson added: “However, we understand that some workers may find these changes unsettling and we are supporting staff through this transition.
“We also encourage staff, where possible, to apply for suitable substantive positions as they become available.”
The hospitals group said move was expected to deliver nearly £5m in savings, helping it meet a wider financial improvement target of £117m.
It also rejected suggestions that patient services would be affected.
“The move to a single outsourced temporary staffing service will not vary the provision of service for patients,” the spokesperson said.
The group said the Department of Health and Social Care had confirmed the decision was not a proposal to change NHS services.