The traffic regulation orders (TROs) were granted for Warner Road, Pennine Way, Cotswold Close, Hambleton Close, Mendip Close, Grampian Way and Malvern Close.
The aim is to prevent traffic from waiting at any time along the roads, helping increase the flow of traffic.
It comes after years of campaigning from local councillors who have received complaints from residents about the number of cars parking on roads in the area.
Many visitors and staff use the roads as an alternative to official car parks but the new orders means double yellow lines will now be brought in.
Coun Phil Lofts has campaigned for the orders for almost five years and says the decision is the first step to making the area safer for all.
He said: “It’s not just the issue of congested streets, it’s also the issue of greater air pollution and the lack of access to pavements for people with prams, or disabled people.
“We have also had reports that ambulances and other emergency services have become stuck while trying to get down these roads which really shouldn’t be happening.
“The roads have become some sort of glorified car park, which isn’t fair on residents.
“We have been working with the hospital to figure out a solution to the issue.
“But, in my opinion, more needs to be done as visitors to the hospital, and hospital staff for that matter, should be able to park their car onsite.”
Coun Sharon Howard praised the decision, but raised concerns that the new measures could push the traffic problem elsewhere.
“I think the orders are very welcome and will help towards the problem in the centre,” she said.
“However, I predict that this will force traffic to park elsewhere in the surrounding areas which isn’t what we want.
“There’s no use just pushing the problem around without dealing with it.”
A spokesperson for Barnsley Hospital said it had put measures in place on-site that the TROs should support.
“We have increased car parking capacity over the last few years and spent a significant sum to upgrade signage and barriers,” they added. “Variable message signs now help drivers to understand where car parking spaces are available.
“Pre-pandemic, the trust was taking further measures such as encouraging staff car share schemes and increasing bike lockers on site as outlined in the hospital’s Active Travel Plan.”