McLaren Construction is understood to have won the 940,000 sq ft build with construction set to start within a few months.
McLaren is believed to have fought-off competition from rivals including Simons Construction.
The megashed, which will be the size of twelve Premiership football pitches, will handle the distribution of around 25,000 nationally available grocery and Home department lines.
David Jones, Waitrose Supply Chain Director, said: “The decision to open our first National Distribution Centre marks a pivotal moment in our supply chain history and reflects our phenomenal growth.
“Waitrose has outperformed the market for five years and we have ambitious plans to open 38 shops in 2014 and continue to expand our online platform.
“By simplifying our supply chain, we improve its resilience and greatly improve our ability to serve our branches now and in the future.”
It would be the second recent warehouse win for McLaren.
The firm started work last November on a £37m distribution centre in Amesbury for TJ Morris.