The move, which is expected to get the go-ahead this week, is aimed at making the workings of the local authority more accessible and open.
Senior officials have appointed broadcasting firm Public-I to provide the webcasts.
The firm, which claims to have pioneered webcasting in the public sector over a decade ago, provides the service for a number of other councils including Edinburgh and Birmingham.
City council deputy leader Archie Graham says in a report that the service will involve live transmission of monthly council meetings plus meetings being archived and bookmarked,
Care will be taken in setting up the cameras to ensure there is no impact on the Grade A listed City Chambers building.
The system will be tested at the council meeting on February 20 with the first to be screened live on April 3.