The site, between the airport and the M1, is next to Pegasus Business Park and is currently used for parking.
The project represents a £114m investment for UPS, an American courier company.
McLaughlin & Harvey starts work this month and is expected to complete in August 2019. Other shortlisted bidders were Galliford Try and Winvic Construction.
In May 2018 UPS opened a 2,000 square metre package sorting and delivery facility at the DP World London Gateway Logistics Park in Essex. At £120m, this new London Hub is one of UPS’s largest infrastructure investments outside of the USA in the company’s history.