Johannsson, the unpopular former fisheries and agriculture minister, takes over from Sigmundur David Gunnlaugsson and is set to take Iceland into legislative elections expected in the autumn.
He and his cabinet were sworn in by President Olafur Ragnar Grimsson in a ceremony at the presidential residence in Reykjavik. Johannsson's new right-wing government is under fire from the start, with the opposition set to hold a vote of no confidence tomorrow and pushing for even earlier elections as the country battles its worst political storm since the 2008-9 financial crisis.
The administration is set to sail through tomorrow's vote, however, as the coalition comprising Johannsson's centre-right Progressive Party and their junior partners, the Independence Party, holds a majority in parliament.
Gunnlaugsson quit Tuesday amid mass protests over a hidden offshore account revealed in the "Panama Papers" leak of millions of financial records, becoming the first major political casualty to emerge from the scandal.
The documents revealed that Gunnlaugsson and his wife owned an offshore company in the British Virgin Islands and had placed millions of dollars of her inheritance there. Gunnlaugsson sold his 50-per cent share of the company to his wife for a symbolic sum of USD 1 at the end of 2009, but he had neglected to declare the stake as required when he was elected to parliament six months earlier.
Gunnlaugsson has said he regretted not having done so, but insisted he and his wife had followed Icelandic law and paid all their taxes in Iceland. Johannsson vowed on the eve of his inauguration that Icelanders would "see the difference" between the two men.
After handing in his resignation to President Olafur Ragnar Grimsson today, Gunnlaugsson was confronted with protesters as he left the presidential residence, brandishing red cards at him and chanting: "Elections immediately, we want to vote!"