The local authority will be one of 26 working with NHS Test and Trace on the new scheme, known as Local-0.
It will mean the council is made aware of new positive cases as soon as they are entered into the national NHS test and trace system.
The council will then be responsible for contacting individuals directly who have tested positive rather than the national service.
It will provide instructions on self-isolation to individuals and their households.
The NHS Test and Trace programme will continue to trace the contacts of individuals who have tested positive, and will continue to provide support to local authorities throughout the process, in order to help stop the spread of the virus as effectively as possible.
The new pilot scheme will help ensure Dudley Council is able to use local knowledge and expertise to determine where people may have caught the virus, which will help identify possible local outbreaks.
Karen Wright, director of public health at Dudley Council, said: "We welcome being part of this national pilot and look forward to working closely with our colleagues in the NHS Test and Trace service.
"We hope being involved much earlier in the process will help us identify where positive cases are occurring and importantly reduce the risk and severity of any local outbreaks.
"We’ll have a team of officers who will be contacting those who have tested positive. To reassure people who are concerned about scam callers, the Dudley Council Plus number 0300 555 2345 will display for those being called.
"I would urge everyone to follow their advice and self-isolate to help protect others in our communities."