The green light has been given for the scheme from Penny Pie Park to Pogmoor Recreation Ground.
The planning process will include a consultation during which members of the public can comment on the plans.
The new foot and cycle bridge is expected to be paid for through grant funding from the Ministry of Housing, Communities and Local Government (MHCLG).
At a cabinet meeting on Wednesday, council leader Sir Steve Houghton said: “This is really welcome and when we consulted on the new road scheme, while not everyone was in favour of the scheme, one thing that did come back was getting a bridge across the railway.
“This was for all kinds of reasons, not least of which we know some young people have been crossing that railway line without any safety measures to get towards Horizon school.
“Hopefully it would deal with a number of concerns and issues around there.”
Cabinet spokesman Coun Tim Cheetham added: “This bridge will be a huge benefit to residents in both the Old Town and Dodworth wards and the wider local area.
“Once this bridge is complete, those who previously used Penny Pie Park will have easy access to even more green space than they did before, and they will also find it easier to access business and other facilities like the hospital on foot, by bicycle or wheelchair.
“By linking the green spaces currently severed by the railway line, and by developing the remainder of Penny Pie Park with much-improved play and recreation equipment, the end result will be a better park than we had before.”