Local universities have 280,000 bed spaces against a student population of 769,500.
The project has been facing criticism from citizens who view it as a waste of money.
Hass Towers in Upper Hill will consist of a 5-star Hilton hotel and a 300 metres high office block.
Prefab technology allows faster construction of buildings.
Africa is undertaking key projects to support its rising population.
The project is expected to cost Sh210 billion.
Africa Integras will build and operate the 10,000-capacity hostel for 20 years.
This follows the completion of phase one of the Two Rivers Mall.
The mall is set on a 4.5-acre piece of land in the Rosslyn suburb on Limuru Road.
The project involves resurfacing Rironi to Mai Mahiu-Naivasha Road.
Nine people were believed to be working at the site when the incident occurred.
Developers will be allowed to build up to 75 floors in high-density areas.
The much-awaited summit will take place on June 12-13, 2025.