Mr. Johnson made the comments at the DUP annual conference in Northern Ireland last November.
"We would be damaging the fabric of the Union with regulatory checks and even customs controls between Great Britain and Northern Ireland on top of those extra regulatory checks down the Irish Sea that are already envisaged in the withdrawal agreement," said Mr. Johnson.
"Now, I have to tell you that no British Conservative government could or should sign up to any such arrangement," he added.
Mr. Johnson replaced Theresa May as Prime Minister in July and repeated his promise that there would be no border in the Irish Sea.
However, on Thursday, Prime Minister Johnson agreed a new treaty with the European Union that involves a border in the Irish Sea.
Mr. Johnson's deal will also see Northern Ireland remain within the E.U.'s customs union and single market.
Some unionists in Northern Ireland described Mr. Johnson entering into a deal with the E.U. as a "betrayal" of not just the Union of Northern Ireland too.
“The scale of the betrayal is shocking," said TUV leader and MLA, Jim Allister.
Mr. Johnson will table his agreement in parliament on Saturday where he hopes to get the backing of M.P.s.
However, the DUP's 10 MPs have said they will not vote for Mr. Johnson's new deal.