Damaged lighting bollards could be replaced by LED lighting columns and the path widened and split to create a dedicated cycleway as part of a £47,000 scheme.
The footpath has been the cause of complaints from both residents and local councillors for years, largely due to the constant vandalism of nine lighting bollards along the route.
The path was meant to form a crucial link between shops in the town centre and the supermarket development to ensure local businesses were not adversely affected by the store.
It was deemed to be so important that Morrisons had to set aside money to pay for a range of enhancement works in the town when it was given planning permission to build its supermarket.
The works included the provision of a pedestrian link between Vulcan Road and the station car park.
But while Somerset County Council upgraded one section at the northern end as part of the redevelopment of land at Mart Road, the rest of the work fell to West Somerset Council.
A legal agreement tied the district authority into maintaining the remainder of the path at its own expense, even though all the land was owned by the county council.
At Wednesday's cabinet meeting, councillors were told the involvement of both authorities had made it more difficult to overcome the constant problem of vandalism.
Any work carried out had to be to a set standard, while the county council would only consider adopting the route - and taking on the maintenance - if a large-scale upgrade was carried out.
Cllr Kate Kravis said there was simply no point continually replacing the damaged bollards only for them to be vandalised again.
"This might seem like a large amount of money to spend on a footpath but we have received feedback and this is the right thing to do," she said.
"We have looked at various options - and this is a great example of three authorities working together to solve a problem."
While the bulk of the £47,000 cost would be covered by £35,000 from Morrisons, £6,000 would come from district council budgets and the remaining £6,000 from a grant from Minehead Town Council.
Minehead member Cllr David Sanders said the footpath was well used and welcomed the proposed upgrade.
"At the moment, due to the condition it is in, it is a blot on the landscape and gives visitors a very poor impression of the area.
"The sooner this is completed the better," he said.
Council chairman Cllr Doug Ross said the state of the path had been one of the most complained about issues he had come across since becoming a councillor in 1995.
"Unfortunately, the originally lighting couldn't cope with the vandals and I hope the budget will allow us to make this a proper dual-purpose path," Cllr Ross said.
Angela Lamplough, the district council's climate change and community liaison manager, said the West Somerset Railway had given permission for the six LED lighting columns to put right up alongside its boundary fence to ensure the path was made as wide as possible.
She said the finer details of the scheme could be finalised next month and work started soon afterwards, providing the full council gave the go-ahead for the project when it met next week.
In a report to cabinet, Ian Timms, the council's corporate manager for housing, welfare and economy, said the work would provide both pedestrians and cyclists with a well-lit route to and from the town centre.
He added: "This application has been considered by Minehead Town Council and Minehead Visioning Group.
"Both these organisations are supportive of this proposal, while the West Somerset Railway is supportive of the new street lights being erected against their fence to enable the increase in the width of the path."