He added: “After five turbulent years of uncertainty, we welcome the news that food and animal imports, and border checks, could be simplified.
“As a major port anything that avoids delays is always welcomed.”
Portsmouth International Port’s building required a £6m contribution from the city council.
A further £17m for the “highly specialist, bespoke facility” was covered by central government, bringing the total cost to £23m.
“We have repeatedly asked for a clear direction on the future of the border control posts, ours is a significant piece of infrastructure that takes up two acres of operational land and has meant a loss of commercial opportunity for the port,” Mr Pitt said.
Safety and security checks started at the site last year, two years after it was built, but much of the facility has remained unused.
Mr Pitt said the local authority had hoped to recoup some of the costs of the council-owned facility through charging for goods to be inspected.
“If the border control post is no longer in use we will be looking for compensation from government to recover the shortfall,” he said.
He added that the council was concerned about the staff in port health but would ensure all changes take place in consultation with them.