Kier, working on behalf of Swansea Council, are beginning to put up internal walls on some of the three floors.
The past few months have seen progress on matters such as demolition of walls and creating a huge new roof light which, in the daytime, will flood the interior with natural light.
The city centre project, in the former BHS store in Oxford Street, is on course for completion this year.
It will bring a range of publicly accessible services, encouraging footfall for local businesses as the council continues its £1bn regeneration programme.
Council leader Rob Stewart said: “It’s great to see progress being made at Y Storfa. When open it’ll be a fantastic location for people from across the city.”
Jason Taylor, regional director at Kier Construction Western & Wales, said: “Y Storfa is progressing well and the building redevelopment is on track to be completed this year.”
Close to car parks, bus stops and cycle routes, Y Storfa will house council-run services such as the contact centre, Housing Options, lifelong learning and the main public library as well as the West Glamorgan Archive Service.
Non-council tenants are set to include Careers Wales, Citizens Advice and Swansea University’s South Wales Miners’ Library.
Funders of Y Storfa include the Welsh Government Transforming Towns programme.
