The Northern Ireland Assembly would have to approve the arrangements first and be able to vote every four years on whether to keep them.
The European Commission says it will “examine [the proposals] objectively”.
Speaking at the Conservative Party conference, Mr Johnson said the only alternative to his plan was no-deal.
He has written to the European Commission’s president, Jean-Claude Juncker, alongside the proposals, saying they “respect the decision taken by the people of the UK to leave the EU, while dealing pragmatically with that decision’s consequences in Northern Ireland and in Ireland”.
Speaking before he saw the plan, Irish Prime Minister Leo Varadkar told the Irish Parliament: “What we are hearing is not encouraging and would not be the basis for agreement.”