Johnson will single out US secretary of state Rex Tillerson for praise for opening the door to dialogue with Kim, which Trump has described as a "waste of time".
He will say that diplomacy is the best way to avoid a nuclear war.
Former CIA Director John Brennan has put the chances of US military conflict with North Korea as high as 20 to 25 per cent.
US officials have been talking about what CNN calls "the increased possibility of a slide into military confrontation with North Korea". CIA Director Mike Pompeo said the US has to act as if North Korea is on the verge of being able to strike it with a missile and act accordingly. US National Security Adviser H.R. McMaster has said Trump wasn't prepared to accept a nuclear North Korea.
US Defence Secretary Jim Mattis kicks off a week-long trip to Asia tomorrow and says he will talk with Asian allies about North Korea and the crisis caused by Pyongyang's "reckless" provocations.
Mattis' trip, which includes stops in the Philippines, Thailand and South Korea, comes just weeks before Trump's first visit to Asia.
Trump has been locked in a war of words with Kim, calling him a "rocket man" on a suicide mission for openly pursuing a nuclear-tipped missile capable of hitting the United States.
Trump, in a speech last month at the United Nations, threatened to destroy North Korea if necessary to defend the United States and its allies. Kim has blasted Trump as "mentally deranged".
Mattis, who has emphasised diplomacy, is expected to meet both his Japanese and South Korean counterparts before meeting all three of them together. He will attend a meeting of defence ministers from the Association of Southeast Asian Nations in the Philippines.
"I will talk with my counterparts, discussing the regional security crisis caused by the reckless DPRK North Korea provocations but also discuss our respect for shared values like sovereignty of the states, their territorial integrity, freedom of navigation through historically international waters, and fair and reciprocal trade," Mattis told reporters.
In his speech, Johnson planned to highlight the importance of the 1970 Nuclear Non-Proliferation Treaty in removing the threat of a "nuclear winter".
He will say: "A new generation has grown up with no memory of the threat of a nuclear winter, and little education in the appalling logic of mutually assured destruction. The memory of Hiroshima and Nagasaki is now literally fading from living memory. The NPT is one of the great diplomatic achievements of the last century.
"It has stood the test of time. It is the job of our generation to preserve that agreement, and British -diplomacy will be at the forefront of the endeavour."
Johnson will restate the "astonishing" and "extraordinary" achievement of the treaty and point out its success rests on nations choosing to "take shelter under a nuclear umbrella" provided by the US.
Johnson will argue that while other military developments, from firearms to fighter jets, have "spread among humanity like impetigo" nuclear weapons remain "the great exception" because of the agreement.
"It has helped avoid what might otherwise have been a Gadarene rush to destruction, in which the world was turned into a great arena of Mexican standoffs, a nuclear version of the final scene of Reservoir Dogs."
- additional reporting AAP
