Al Jazeera's correspondent Haru Mutasa, reporting from Antananarivo, said people in the capital were eagerly waiting for the 34-year old to reveal details on how he will rule.
"The people here know that some factions in the military supported the former president and that some factions supported Rajoelina.
"People say that if these two don't work together to maintain stability, there could be chaos in the streets."
Ravalomanana has not been seen in public since he stepped down and ceded authority to the armed forces on Tuesday.
"Some speculate that Ravalomanana ... may be fleeing for his life," Mutasa reported.
Rajoelina has repeatedly accused Ravalomanana of being a dictator and of misusing public funds. In turn, Ravalomanana's supporters call Rajoelina a troublemaker bent on taking power illegally.
'Abuses' of power
Razafimahileo Benja, a Rajoelina supporter, told Al Jazeera: "The plan is to clean all of Ravalomanana's abuses in management. We will try to clean everything in the country as much as we can.
"Corruption is a big issue... Perhaps we won't succeed in avoiding it every time, everywhere, but we will try to set up better governance. That's the main challenge."
The embattled former president, whose palaces were surrounded by the military on Monday, announced that he was dissolving the government and handing presidential powers to a directorate of high-ranking military officers.
The military, in turn, handed power to Rajoelina, who was dismissed last month by Ravalomanana as the mayor of Antananarivo.
Hyppolite Ramaroson, a navy admiral and the most senior military official, told reporters on Tuesday: "We give full powers to Mr Andry Rajoelina to become president of the high transitional authority."
Thousands of supporters cheered as Rajoelina travelled to the presidential office compound, which had been seized by troops on Monday.
"This is a David versus Goliath victory," one excited opposition supporter yelled.
'Road remains tough'
But Rajoelina warned that "we are now free but the road ahead remains rough".
"Now we are in for quite a rough ride because the new government is going to be illegitimate"
Stephen Ellis, historian
"The best gift we can give to Malagasy people is the commitment to protect their interests," he said.
But Stephen Ellis, a historian, told Al Jazeera Rajoelina may face some hurdles in winning the support of the country as a whole.
"[His claim to power] is clearly unconstitutional and there is going to be a period of instability," he said.
"Now we are in for quite a rough ride because the new government is going to be illegitimate."
|At least 135 people have been killed since the political crisis began in January [Reuters]
At least 135 people have been killed since the country's political crisis began in January, most of them when security forces cracked down on anti-government protests at the order of Ravalomanana's government.
The crisis, with Rajoelina leading anti-government demonstrations, has also damaged the country's nearly $400m-a-year tourism sector.
Adding to the country's problems may be ostracism by the African Union, which had warned Madagascar's military against handing power to Rajoelina.
Jean Ping, the African Union (AU) commission chairman, said before the military's decision that any taking of power by non-constitutional means would be considered a coup d'etat. According to the AU charter, coups or unconstitutional changes of government are cause for automatic suspension.