UK-based developer Bouygues Development has submitted an application to Portsmouth City Council to replace the 1960s era Brunel House with a new 40-storey skyscraper, the Portsmouth Shard.
The plan will require the vacant Brunel House to be demolished and a new building to be constructed.
The 118m tower will form part of The Hard waterfront redevelopment between HMS Warrior and Gunwharf Quays.
The skyscraper will feature around 330 private residential units and accommodation for about 500 students, as well as a restaurant, café and multi-storey car park for 300 vehicles.
Portsmouth Society planning officer John Holland said it is an exciting proposal.
"The old Brunel House has been an eyesore for too long," Holland said.
Bouygues Development managing director Nicolas Guérin said the submission of the Brunel House planning application marks an important step in the creation of a scheme that will be great for Portsmouth.
"The scheme will provide a vibrant and exciting street frontage while assisting in the wider regeneration of The Hard," Guérin said.
"We look forward to working with the planners at Portsmouth City Council to achieve planning and bringing forward a scheme which will provide important jobs and an economic boost."
Bouygues Development had earlier dropped its plan to include a hotel and did not want to add affordable housing to the plan, as the cost would make the proposed development non-viable.
Portsmouth City Council has asked locals to submit their views on the plans by 23 May.