Community leaders hope the work, which was approved at a planning committee meeting on Tuesday will help tackle flooding issues in the area.
The culvert runs through a railway embankment near Bridge Avenue and Myrtle Glade.
A report to the planning committee said: “This application relates to a 70-metre-long section of culvert that carries Wyrley Brook through a railway embankment at the northern end of the Cheslyn Hay and Great Wyrley Development Boundary. It has been submitted by Network Rail and the proposal is to reconstruct the damaged culvert, which is in urgent need of repair due to loose brickwork and cracking within the culvert barrel.
Committee members voted unanimously to approve the application.
Councillor Kath Perry, who represents the Great Wyrley ward, said: “I welcome this application. You’re well aware of the issues we have with flooding in Great Wyrley.
“I know this area well – I’ve even been out and had another look today to see what’s going on at Myrtle Glade and Bridge Avenue. I hope that it will be the start of many more organisations connected to the Wyrley Brook to stop the flooding we have in Great Wyrley.”
Committee chairman Mike Lawrence, who also represents Great Wyrley, said: “We have spent many hours over many years trying to get work done on this culvert and I’m glad to see it starting now. It’s essential maintenance – if we don’t let it happen we’ve got a risk of flooding in the area.
“To me it’s a no-brainer.”