Due to the asbestos contamination, most of the materials from the original auditorium area of the building were unable to be salvaged.
For the next three to four weeks, the council said surrounding residents and businesses could expect some work noise and heavy vehicles moving in and out of the site during the day.
The building and its direct surroundings would be fenced off from public access.
Although the Soundshell building was located on Lakefront Drive, the road would still be open.
In 2015 the Soundshell was closed after a number of issues - including structural integrity, general disrepair and earthquake proneness - were identified, meaning it was uneconomical to do the work needed to make the original building safe, as well as bring it up to a usable standard.
Following public consultation, the upgrade of the site was then included in the council's 2018-2028 Long-Term Plan as part of the Lakefront redevelopment.
Once the building has been fully removed, the concrete slab will be taken away and the ground levelled.
