The £10 million project will see the refurbishment of Conavon Court in Blackfriars Street and the construction of a 10-storey glazed extension.
The building was acquired 20 years ago by the scheme's developer Adam Geoffrey Management, and has suffered from gradual deterioration. It is hoped the development will give it and the surrounding area a new lease of life.
The warehouse was built in 1866. It has a Venetian Palazzo facade and is regarded as having the most architectural quality on Blackfriars Street.
The extension will be mainly glazed in a random pattern of fritted glass. According to the Manchester-based practice, there will be clear glazing to the rooftop pavilion and circulation areas, including the lift shaft, revealing movement inside the building.
Architect Richard Drinkwater said: 'It is the culmination of three years' work to get the scheme to approval stage. It marks a major step forward for us, and obviously we are delighted by the decision.
'As well as using glass, we are also going to use traditional materials in a modern way, such as lead panels to the service cores, to help develop the relationship between the listed building and the extension.'
An atrium will be created between the rear of the existing building and the new extension, containing glass lifts on the external face at higher levels.
Drinkwater added: 'The effect of travelling in the lifts will be spectacular as one passes from inside to outside, with magnificent views of Manchester city centre and a panorama across Salford.'