Work on the 1,680-place category C resettlement prison is scheduled to begin next month and to be completed by autumn 2021.
The facility will have seven house blocks with over 60,000m² of accommodation facilities and ancillary buildings.
It will feature windows with no bars and smaller wings holding just 20 men in line.
Kier is working with Mace as client project manager, WTP as the cost consultant and Pick Everard supported by HLM as the architects.
The new prison is part of the Government’s Prison Estate Transformation Programme, which is reforming and modernising the prison estate to ensure conditions are suitable for rehabilitation of offenders while reducing crowding across the estate.
Along with Wellingborough, the programme will deliver a new prison at the former HMP & YOI Glen Parva in Leicestershire and a new house block at HMP Stocken, in Rutland.
Prisons Minister Rory Stewart said: “I am committed to the building of up to 10,000 modern and decent prison places to replace old, expensive and unsuitable accommodation, and the start of work at Wellingborough is an important step forward.”