The blocks are adjacent to Africa Oil's blocks 10BB.
"Existing gravity data on Blocks 12A and 13T suggests that the proven Lokichar basin and other prospective sub-basins and known strong leads in Block 10BB may extend onto these new blocks," Africa Oil and Alberta Oilsands said in the statement issued late on Wednesday.
The Production Sharing Contracts covering the new blocks are dated September 2008 and have an initial exploration period of three years.
Africa Oil has agreed to provide the state-owned National Oil Corporation of Kenya a 7.5 percent working interest throughout the exploration phase and the government maintains its back-in rights for a 15 percent paying interest.
The East African Rift Basin system is one of the last of the great rift basins to be explored. Discoveries have been made in east Africa, including Uganda's Albert Graben, Tanzania's offshore Songo Songo gas wells, and Mnazi Bay in the south of the country.
Africa Oil is exploring for oil and gas in Kenya, Ethiopia and Somalia's Puntland region.
"The acquisition of these two new blocks continues the consolidation of our land holdings around Block 10BB, which is located within the highly prospective East Africa Rift Trend," said Keith Hill, Africa Oil's CEO.