The board of directors at Shrewsbury and Telford Hospital NHS Trust (SaTH) approved the new role during an online meeting yesterday.
David Brown, one of the trust's non-executive directors, was also appointed for the job.
Dr Catriona McMahon, chair of SaTH, which runs Royal Shrewsbury Hospital and Princess Royal Hospital in Telford, told board members: "This is highlighting the requirement for trusts to have wellbeing champions whose job is to constructively hold the board to account with regards to how we are addressing particularly NHS staff wellbeing and what we're doing to reduce sickness levels.
"I am delighted to say that David Brown has been appointed as the wellbeing guardian for our trust.
"I look forward to the support and challenge we will receive."
In a report to the board setting out the proposal, she said the last year of the Covid-19 pandemic had "exacerbated the need for staff support".
The report said: "We believe that the introduction of a board level ‘wellbeing guardian’ would send a message to our colleagues illustrating how seriously we, as leaders of the organisation, take their wellbeing and want to support their needs.
"We believe that this role would be ideal for a non-executive director to undertake.
"It is proposed that the wellbeing guardian will take an assurance role, in which they look at the organisation’s activities through a holistic health and wellbeing lens.
"Their purpose would be to question decisions [made by the board] which might impact on the wellbeing of our colleagues; challenge behaviours which are likely to be detrimental; challenge the board to account for its decisions and their impact on the health and wellbeing of our NHS people; and remind the board to consider any unintended consequences of organisational actions and review them with a view to mitigating these."