The man at the head of Pinderfields, Pontefract and Dewsbury hospitals says he wants them to be collectively classed as outstanding by 2022.
Martin Barkley, the chief executive of Mid Yorkshire Hospitals NHS Trust, said that the organisation could be recognised as one of the country's best within three years if further improvements are made.
The Care Quality Commission (CQC) rated the trust as 'requires improvement' following an inspection last year, but recognised substantial progress in a number of areas since its previous visit in 2017.
In a wide-ranging interview, Mr Barkley said that developing staff satisfaction within the hospitals was the key to improving all aspects of healthcare.
Asked how long he believed it would take for the trust to achieve the top rating from the health watchdog, Mr Barkley said: "My ambition is three years from now.
"I'm really confident that with the great staff we've got here, we can achieve it.
"The sort of loyalty and commitment they have, despite all the difficulties there have been, is absolutely humbling.
"If we can support them better and empower them better, it will lead us to achieve that rating of 'outstanding'."
The chief executive said that year-on-year improvement in the staff satisfaction survey was one of the things he was most pleased about after three years in charge of the trust.
He added: "All the evidence in the western world is that the quality of patient experience is inextricably linked to staff experience.
"So improving staff experience will help us retain staff and will help us recruit new staff. All of this will benefit patients, which is what it's all about."
Pinderfields Hospital, on Aberford Road in Wakefield, has been beset by recent troubles with staff parking, with employees being penalised for using patient spaces when the staff section is full.
The issue has drawn criticism from trade union UNISON and Mr Barkley admitted that around 800 hospital workers at the site are awaiting permits, a situation for which he apologised for.
He said: "That's obviously really, really poor.
"I genuinely sympathise with staff and I'm really sorry, because I know that it's a concerning problem and it's adding to their journey times.
"One of the paradoxes is that we have more car parking spaces than any other general hospital in the region, but around Pinderfields there's very little off-street parking."
The trust, which has a deficit of around £30m, is still trying to secure finance to create extra parking spaces which were given planning permission last year. Mr Barkley said that delay was, "Frustrating to put it mildly", and he wanted to see the situation resolved as quickly as possible.
Mr Barkley is celebrating 25 years in NHS management this April. In an era where the health service is widely believed to be chronically underfunded, he said that new medical advances made and artificial intelligence were reasons to be optimistic about its future.
He also said that a nationally dwindling workforce was a bigger problem than cash.
"Vacancies I think will be a more limiting factor than money going forward," he added.
"The recruitment gaps in nursing staff first appeared around eight years ago and that gap has never been bigger than it is now.
"We have around 200 registered nurse vacancies at the moment and many other trusts are in a similar position.
"We've set up a virtual nursing school with the University of Bradford recently, which will start to bear fruit for us in two or three years time. But that's a local solution and it still doesn't resolve the national shortage."
Mr Barkley said politicians were right to impose time-sensitive targets for patient care, despite NHS trusts struggling to meet several of them in the current climate, because he believes they have raised standards significantly.
And he said it would be "up to the public at the ballot box" whether or not they want to see the NHS continued to be funded sustainably by tax, a system he wholeheartedly supports.
He added: "I'd hate to see a system, like in the United States, where people are scared to get ill.
"The NHS gives amazing value for money. Compared to almost any other health system in the world it's the most efficient, and I think that will continue."
Local Democracy Reporting Service