Bekale was appointed after a decree to that effect made public late in the night of Friday into Saturday.
The announcement was made by the secretary general of the Gabonese presidency, Jean-Yves Teale.
Mr. Bekale succeeds Emmanuel Issoze-Ngondet, named "mediator of the Republic".
The new Prime Minister had served severally as minister under President Ali Bongo.
Shortly before his appointment, the National Assembly elected Faustin Boukoubi as its president.
It comes barely six days after a group of Gabonese soldiers launched an unsuccessful coup against Mr Bongo who is still convalescing in Morocco after being taken ill last October.