The DJ has been back broadcasting his breakfast show from Dundee this week.
The six-storey block will be named James Thomson House after the late city architect.
The two-bedroom flat was marketed at £150,000.
Sabinah Islam, 53, died in hospital six weeks on from the blaze in Fintry.
Gwen Ferguson had been working in a department where she investigated internal thefts when she was caught.
The "alarming" incident saw the person take off with 14 people's personal data.