The Welsh government began constructing the post with Kier Construction, the main contractor on the project, in March 2024 and it was anticipated to be completed by autumn 2025.
Holyhead is the busiest Irish Sea ferry port, handling more than 75% of imports from Ireland to Great Britain.
The site planned to create jobs in the local area, with up to 30 employees expected to staff the site over a 24-hour period.
The Welsh government said it remained committed to providing sufficient notice for traders and delivery partners should any new border checks need to be introduced.