The new building, replacing Beverley Business Centre, will be split between offices and light industrial uses and aims to provide employment for 85 full-time staff.
Applicants, East Riding Council, say it will be a "landmark" building offering "superior" facilities for new and existing businesses.
The proposals show a two-storey building along the Grovehill frontage to the north, reducing to a single storey along Beck View Road frontage to the west.
The car park will provide 121 spaces for building users and visitors, plus five dedicated disabled spaces adjacent to the main entrance, three spaces for electric cars and space for motorcycles.
Vehicles will enter from Beck View Road and exit onto Grovehill Road.
East Riding Council confirmed the cost of the business centre at £3.95m
The site was previously occupied by the County Council engineering depot and ambulance station.
Outline planning permission was recently granted for the proposals.
The application for full planning permission is due to be considered by councillors at County Hall next Monday.