Rajoelina, who was impeached by MPs after fleeing abroad at the weekend, has condemned the takeover and refused to step down despite "Gen Z" demonstrations demanding his resignation and widespread defections in the security forces.
Randrianirina has told Malagasy citizens that the military has taken power and dissolved all institutions except the lower house of parliament or National Assembly.
"We will be sworn in soon," the army colonel told a press briefing on Wednesday, a day after the High Constitutional Court invited him to serve as president of the former French colony.
"We took responsibility yesterday."
Two sources close to him earlier told Reuters he would be sworn in as president in the next day or two.
Randrianirina said on Tuesday that a committee led by the military would rule for up to two years alongside a transitional government before organising new elections.
"There must be an oath-taking" to make his position official, Randrianirina told the Associated Press on Wednesday at his unit's barracks while flanked by fellow officers.
"We are staying here for at least 18 months, at most two years."
Randrianirina said the military leadership was "accelerating" the appointment of a new prime minister "so that the crisis in the country does not last forever".
He did not give an exact time frame for that to happen.
The protesters, led by youth groups calling themselves "Gen Z Madagascar," have demanded better government and job opportunities, echoing youth-led protests elsewhere in the world.
Among other things, the Madagascar protesters have railed against chronic water and electricity outages, limited access to higher education, government corruption and poverty.
Randrianirina was a commander in the elite CAPSAT army unit that played a key role in the 2009 coup that brought Rajoelina to power but broke ranks with him last week, urging soldiers not to fire on protesters.
Rajoelina fled Madagascar on Sunday aboard a French military plane, security sources told Reuters.
He has said his life was at risk and is now believed to be in Dubai, according to three diplomatic and opposition sources.
The 51-year-old former DJ himself rose to power in a coup in 2009 on the back of youth protests, becoming the world's youngest head of state at 34.
But promises to improve living standards and eradicate corruption were never fulfilled.
Madagascar, where the average age is less than 20, has a population of about 30 million, three-quarters of whom live in poverty.
Between its independence in 1960 and 2020, GDP per capita plunged 45 per cent, according to the World Bank.
with AP
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