Bongo, who died in Spain, was reportedly being treated for cancer. On Monday, Jean-Eyeghe Ndong, the prime minister, said he had died of a heart attack.
Rogombe, 66, will have most of the powers of an elected president apart from authority to dissolve parliament or to hold referendums, court officials said.
She is constitutionally ineligible from standing in the presidential poll, due to be held between 30 and 45 days.
The government acted fast to avert a power vacuum after Bongo, Africa's longest-serving head of state, died in a Barcelona hospital.
Rogombe was born in 1942 at Lambarene, 240km southeast of Libreville.
A trained lawyer and member of the Gabonese Democratic Party (PDG) founded by Bongo, Rogombe was elected senate president for six years last February.
"We saw the ceremony with some satisfaction because she's a woman but there was also plenty of emotion and tears because of the president's death," Francoise Makaya, a PDG politician, said.
In a country observing 30 days of mourning, national and international tributes will be paid until June 18, when the late president's body will be taken for burial to his native Franceville region in the east.