The billionaire businessman blamed the move on his predecessor Barack Obama, even though the decision was agreed by George W Bush's administration.
Johnson, a Trump appointee, also said the new embassy was entirely paid for by the sale of other London properties and "did not cost the USA taxpayer a cent".
Prime Minister Theresa May invited Trump for a state visit when she met with him at the White House soon after he took office past year.
On Friday night, a spokesman for the US embassy said: "The US chancery in Grosvenor Square had aged beyond its ability to be improved to current security and life safety standards without extensive investment in infrastructure that would require appropriated dollars".
The "strong and deep" partnership between Britain and the USA "will endure" despite Mr Trump's cancellation, a spokesman added.
Many British politicians have voiced their opposition to Trump being granted a state visit, and say the invite should be recalled.
Since then, however, the president has indicated he does not want to take up the invitation if he is going to face mass demonstrations and it had been expected he could make a low-key working visit rather than a trip which involved all the trappings of a state occasion.
The new one is in Nine Elms, a former industrial area on the south side of the River Thames that is being redeveloped as a commercial and residential district.
Trump acknowledges 'tough' language but appears to deny 'shithole' remark
And Idaho Republican Mike Simpson told The Associated Press that Trump's remarks were "stupid and irresponsible and childish". Trump later tweeted comments about "taking them out" - referring to Haitians - were "made up" by Democrats .
London Mayor Sadiq Khan, an outspoken Trump critic, welcomed the trip's cancellation.
Upon hearing the news that Donald Trump would not be opening the USA embassy in London next month, waxwork museum Madame Tussauds stepped in to provide an alternative. "Bad deal. Wanted me to cut ribbon-NO!", Trump tweeted. The move, which ended a 200-year USA association with London's Grosvenor Square, was part of American efforts to secure diplomatic staff in compounds - a push tied to terror concerns after al-Qaida bombings at two US embassies in East Africa a decade ago.
The mayor of London - who has been criticized by Trump in tweets - said Trump appeared to have "got the message from the many Londoners who love and admire America and Americans but find his policies and actions the polar opposite of our city's values of inclusion, diversity and tolerance".
Relations between May and Trump became strained in November after he re-tweeted anti-Muslim videos posted by a British far-right group.
May's spokesman said the president was wrong to retweet the group's content - prompting Trump to tell May in a tweet that she should focus on "the destructive Radical Islamic Terrorism that is taking place within the United Kingdom" instead of him.
"His visit ... would without doubt have been met by mass peaceful protests", Khan said.
There was initially confusion as Downing Street was unable to say whether the Foreign Secretary was speaking for the Government when he said Mr Khan and Jeremy Corbyn were putting the "crucial relationship at risk". "The opening of the U.S. embassy is a matter for the United States".