The building is now 85% complete and its inauguration is slated to take place by year's end, local media sources said.
The project, which was cancelled multiple times in the past because it was judged "against the public interest", will significantly alter the architecture in the square, where demolition and remodeling work has also begun on a symbolic building of Republican Turkey, the Ataturk Cultural Centre.
In the coming days the mosque's cement cupola is expected to be completed.
Its 30-metre height will put it at the same level as the two historic churches in the area.
The interior and minarets will follow.
In addition to space for prayer, the structure will include a conference room and an underground parking lot with 180 spaces.