Developer Town Centre Securities has appointed contractor BAM Construction to transform the 1960s office building into a modern glass-fronted structure.
Work on the ten-storey Merrion House, which until recently was occupied by Leeds City Council employees, is scheduled to be finished by the end of 2017.
The scheme includes a part new-build over seven and eight storeys to increase the floor area and capacity.
BAM’s construction director Kelvin Pollard, said: “BAM’s specialist services engineering business will help us deliver what will be a striking transformation.”
Mr Pollard added: “This is going to be a very visible building as you enter the city of Leeds from the north.”