The £12 million project, for developer Urban I, will include the tower itself, two new five-storey apartment buildings, the refurbishment of a four-storey townhouse, and the conversion of the grade II-listed Castle House.
The brownfield site, which faces the River Don and was earmarked by the council as a 'gateway site', was previously used for retail and warehousing.
Peter Cartwright, a director at Cartwright Pickard, said he was pleased to have taken on the job.
'Our intention is to create a variety of distinctly contemporary buildings,' he said.
'The form and position of the tower will be a strong urban landmark, and it will have its own clear identity.
'We will also be bringing a listed building and an important local monument back to life,' Cartwright added.