The store is being developed now with a view to opening in June.
It follows a deal by property investment and development company Dunmoore with CBRE Investment Management.
Lidl has agreed a 25-year lease.
The supermarket development marks the start of the second phase of development at the business park that will provide 250,000 sq ft of industrial and business accommodation.
Dunmoore owner and chief executive Jeff Hobby said: “The progress we have made with the development in such challenging times has been excellent and this deal is testament to our understanding of the ever-changing market and requirements.
“With continued high levels of demand, we look forward to providing further modern flexible business space for the local area.”
David Holt, partner of WHY Property Investment which advised CBRE in the deal, said: “The excellent quality of development at Billingshurst Trade Park meant the proposed Lidl unit was much sought after and will be a great addition to the scheme.”
The sale coincides with Dunmoore’s disposal of Billingshurst Trade Park to Aegon Asset Management for £17 million.