Hackney's planning committee has approved the mixed-use scheme, which also involves the renovation of a run-down listed Art-Deco building on the site.
This project, for developer Groveworld, will have a serious impact on the City Road area of Shoreditch, close to the Old Street roundabout.
When complete, the development will include the new tower, 276 residential units, of which 30 per cent will be affordable, and 6,500m 2of commercial space.
Terry Farrell said he was delighted to have won the planning permission, which had involved lengthy negotiations with both CABE and English Heritage.
'The redevelopment of Eagle House and the adjacent land represents a key milestone in the transformation of this part of the city,' he said.
'We have worked hard to design a building that positively contributes to the street, both by providing active frontages and a vibrant public space - an identifiable and elegant addition to the skyline,' he added.