The East End firm is to submit an outline planning application for the scheme, designed by architect Michael Squire and Partners, to Tower Hamlets Council next week.
It plans to start on site late this year or early next year, subject to receiving detailed planning permission. A Ballymore spokeswoman said the project would start even if a tenant had not been secured for any of its 67 000 m² of office space.
The company said there is a demand for office space in the area, with 1980s blocks that stood empty for years now full.
Ballymore's tower will be on the site of Building's former office on the Isle of Dogs, which has been empty since an IRA bomb devastated the area in early 1996.
The 202 m high tower will be shorter than the nearby Canary Wharf Tower and the HSBC HQ now under construction.
GVA Grimley is Ballymore's planning consultant, its QS is Davis Langdon & Everest, its structural engineer is Ove Arup & Partners and its services engineer is Roger Preston & Partners.
US bank Salomon Smith Barney was this week linked to a move to Canary Wharf. It may be housed in a tower being built for Citicorp.
