The country also reopened its borders as the government paved the way for a smooth presidential succession after the death of Bongo, who ruled for 41 years.
A senior judge announced yesterday that the country's constitutional court had taken the decision. Rogombe, 66, would "provisionally" exercise power and take an oath today "in the presence of parliament and the constitutional court," presiding Judge Marie-Madeleine Mborantsuo said.
Elections would then be held between 30 and 45 days later.
"The important thing is to respect institutions and the memory of president Bongo," Communications Minister Laure Olga Gondjout told journalists, after some ministers left the cabinet meeting in tears.
"We're strictly following the constitutional route, contrary to supposition and Machiavellian plans attributed to one person or another, particularly the defence minister," Interior Minister Andre Mba Obame said.
Bongo's son Ali Ben Bongo, 50, Gabon's defence minister and favourite to succeed him, called Monday for public calm and closed the borders in the wake of his father's death.
"We're following the constitution at the pace of a forced march since the Bongo clan left no time to prepare anything else," a source close to the presidency added. "There's no major problem, because everyone wants peace."
But the same source warned that "organising democratic elections within 45 days is impossible" because of a lack of an accurate electoral roll.
Bongo's death at 73 was announced by the prime minister Monday in Barcelona, Spain, where he had been undergoing treatment since early May in a private clinic for intestinal cancer.
Many Gabonese mourned the only president they had ever known, whose body was due to be repatriated tomorrow, with official ceremonies set to be held from Friday to Monday. Most shops and markets were open as normal in a calm capital, with police and troops posted outside strategic official buildings and embassies.
"It's like a normal Tuesday," said a worker in a shopping centre. But a car park guard at Libreville's biggest supermarket said that Monday's announcement was followed by "a rush to stock up on food," in case of a curfew. "It was madness."
The frontiers were reopened yesterday and the defence ministry said that there would be no curfew, though public buildings would still remain under watch. Flags flew at half-mast; special broadcasts were aired on state radio and television, while mourning will last for 30 days.
The government has stressed the importance of unity and credited Bongo with bringing it to the former French colony, a patchwork of ethnic groups.
US President Barack Obama praised Bongo's "commitment to conflict resolution," while African leaders hailed the elder statesman and peacemaker, particularly in central Africa.
"Bongo has contributed enormously to the African continent through his involvement in peaceful resolution of conflict in the Central African region and the continent as a whole," South Africa's foreign ministry stated.
President Joseph Kabila of the Democratic Republic of Congo said the death of "this great statesman who put his stamp on the history of contemporary Africa was a great loss".
Bongo came to power in 1967 with French support to rule over a nation that grew rich on oil - pumped by French firm Elf that long ran a state within a state - and maintained wealthy elite while most of the 1.5 million population remained poor.
In his last months, Gabon's relations with Paris soured over a French probe into Bongo's luxury residences in France and a court order to freeze his bank accounts, based on allegations the properties were acquired with embezzled funds.