Printful will take over the sprawling 'Antar 2' unit next to Wolverhampton's Discovery Park, on Headway Road, off Wobaston Road, in a move that will create up to 150 jobs.
The firm, which has its head office in Charlotte, North Carolina, has three existing European fulfilment centres – two in Latvia and one in Spain, with another due to open in Poland.
It also has other sites around the world.
Details of the plans are revealed in a design statement accompanying an application to Wolverhampton Council for the installation of 11 external flues on the roof of the unit.
It says the 88,377sq ft site is undergoing a full refurbishment having been occupied by another firm for more than 10 years, and that Printful intends to take over the building from August 2021.
The statement adds: "Printful is set to initially invest over £2.6 million in the fulfilment centre in Wolverhampton.
"It will be the first Printful facility in the UK and will provide local fulfilment for services such as DTG (direct-to-garment), embroidery, and printing for home and living items, eventually adding other options.
"The new fulfilment centre will bring about 50 jobs in the first year of operations, and up to 150 jobs once the site operates at full capacity.
"Wolverhampton is in a strategically great location and has well established infrastructure links, which allows Printful to provide local fulfilment and deliveries within the country in two business days or less.
"Printful intend to occupy the building to provide their services which essentially includes four different production processes including Direct to Garment printing (main process), poster printing, ink printing on mugs, and embroidery.
It adds that the flues are required to release hot air that builds up during one of the manufacturing processes used by the business.
Printful was founded in 2013 and employs more than 700 staff in Europe and more than 1,800 people globally.