The Foreign Secretary spoke out after facing calls to resign for saying one of the two options being considered by Downing Street was “crazy”.
It comes ahead of the Government’s “war cabinet” meeting on Tuesday to thrash out the proposals.
The customs partnership scheme, believed to be favoured by the prime minister, would see the UK collect EU tariffs for goods coming into Britain on behalf of Brussels.
But hardline Brexiteers favour a maximum facilitation, or “max fac”, scheme that would use technology and a “trusted trader” plan to reduce customs checks.
Mrs May defended the divisions, writing in an article for The Sunday Times: “I have proposed different options for a new customs arrangement with the EU and the government will continue to develop them during the negotiations.”
Later, Mr Johnson insisted he thought that position was “completely right”.
“I thought the prime minister’s piece in the Sunday Times really set it out very clearly,” he said after talks with his French counterpart in London.
“What we need to do is, as she said, come out of the customs union in such a way as to enable us to have frictionless trade with no hard border in Northern Ireland.
“And to do unhindered, unimpeded free-trade deals with the rest of the world.
“We think that is possible, she thinks that is possible, so that is the way forward.”
Pressed on calls by Tory MPs including former attorney general Dominic Grieve to resign, Mr Johnson said: “I think that the prime minister’s position, that I have now twice applauded, is the right one.”
Groups of backbenchers have been summoned to Downing Street by Mrs May’s chief of staff Gavin Barwell to explain the two options under consideration.
The “war cabinet” will convene again on Tuesday to discuss ministers’ work on them – but an announcement is not expected.