The long-awaited project will separate emergency and planned care in the county, with Royal Shrewsbury Hospital housing the main A&E department and consultant-led women and children’s services.
Telford's Princess Royal Hospital will become a centre for planned care and will have a scaled-down ‘A&E Local’.
Funding for the next stage of the plans has been awaited, before engaging external professionals to help complete the outline business case.
The cash is being sought to engage architects, mechanical and electrical engineers and specialists in civil engineering, project management, transport and healthcare planning, to put in place final designs and planning proposals to enable applications to be made for the work.
Health minister Ed Argar confirmed that £6m worth of funding has been approved in principle to take the Future Fit plans forward, after south Shropshire MP Philip Dunne raised a question in the House of Commons.
Mr Dunne said: “I am pleased that Minister Ed Argar confirmed draw down can begin for the significant investment into improving Shropshire’s acute hospitals.
"I know everyone is very focussed on tackling the Covid pandemic right now, so it is pleasing that the green light from both the NHS and Department of Health and Social Care has now been given to proceed to the outline business case.
"Shropshire MPs wrote last month to the Secretary of State.
"I raised the issue again at health questions in the Commons, urging Ministers to dig into the intray and excavate the funds to enable this vital capital project to get back on track.
"The news that this approval is on its way is extremely welcome.
"It will help ensure that the NHS in Shropshire can pull together once more to modernise our acute care for future generations.”
Hospital bosses say Future Fit, which is now called the "hospitals transformation programme", will deliver safer care and better outcomes for patients, reduce cancellations of planned care and the amount of time people stay in hospital.
Louise Barnett, chief executive at The Shrewsbury and Telford Hospital NHS Trust, which runs the hospitals, said: “We welcome the announcement from the Department for Health and Social Care that £6m of funding has been approved in principle for the hospitals transformation programme.
"We look forward to continuing to work with our partners and local MPs as we further develop our plans.”
The project was originally earmarked to cost £312 million, but due to inflation and other costs that figure has escalated to much more.
Sir Neil McKay, chairman of the county’s sustainability and transformation partnership, said earlier this year that discussions were ongoing with the NHS about the cost of the project.