"I spoke to him [Johnson]", Trump said on Friday. "I predict he will be a great prime minister... he and I will spend a lot of [time together]".
Trump added that he and Johnson are already working on a free trade agreement between the United States and the United Kingdom.
The latter became the new prime minister of the United Kingdom on Wednesday, replacing Theresa May, who resigned over her failure to ensure Brexit within the set time limits.
Johnson, who has previously served as the mayor of London and UK foreign secretary, has championed free trade and has been a leading figure in the Brexit campaign to pull the United Kingdom out of the European Union.