During the first day of his trip to the US, Mr Varadkar said Mr Johnson and UK Brexit Minister David Davis would be "very welcome to visit the Border" and that such a trip could prove "helpful".
The Irish border remains a key talking point during Brexit negotiations.
Taoiseach Leo Varadkar has said it would be "helpful" for leading Brexiteers such as Boris Johnson to visit the Irish Border to see for themselves how it is now "invisible".
The British government wants to leave the customs union and has rejected a so-called "backstop" option put forward by the EU which would see Northern Ireland remain in the customs union if a comprehensive deal can't be agreed with the UK.
Mr Varadkar says certain tensions could be re-ignited by a hard border.
The Camden solution: how ridiculous are Boris Johnson's claims on the Irish border really? "And to see that it is invisible".
"The reality is, I don't anticipate a return to violence, but if you do have physical infrastructure, if you do have cameras and signs and border posts then you know those things will become targets", he said.
New research on a smart border between Northern and the Republic of Ireland continues.
It comes as UK Chancellor Philip Hammond restated his government's commitment to avoiding a hard Border, and admitted there was no model anywhere in the world for the kind of post-Brexit arrangements the UK is seeking. And then what do you do?
Remarks by Mr Johnson, the British foreign secretary, comparing the 500km Irish Border to the congestion charge boundaries in London were met with derision in recent weeks. "If I was Northern Ireland Secretary and this report came on to my desk, its next stop would be the bin". "If Brexit is a threat to that, everyone is entitled to keep an open mind about whether it's the right path for the country".