The PM said the new line-up brought in "talent from across the whole of the Conservative party".
Johnson, the former foreign secretary, secured 92,153 votes against 46,656 of his rival Jeremy Hunt in the battle for 10 Downing Street.
Johnson becomes the 14th Prime Minister to be appointed by Queen Elizabeth II, the 55th to hold the post of British PM and the third in fairly quick succession since Britain voted to leave the EU in June 2016 - following on from David Cameron and Theresa May.