He will be the head of state until next year's poll in May in order to fulfill what would have been the rest of Yar'Adua's term.
Under an unwritten power-sharing agreement within the ruling People's Democratic Party (PDP), the presidency should rotate every two terms between the predominantly Muslim north and Christian-majority south.
The convention was introduced in order to avoid an imbalance of power between the two regions.
The president's decision to select Sambo, a relative newcomer in the Nigerian political arena, has surprised many analysts.
Jonathan has not ruled himself out of running for president, although he said in April that he wanted at least three months to see how his reforms are carried out.
But a bid for the presidency by Jonathan, a Christian from the south, would be highly controversial because it would be widely seen as upsetting the geopolitical balance of power.
Yvonne Ndege, Al Jazeera's correspondent in Abuja, the Nigerian capital, said: "There has been a lot of political turmoil about who the vice president nominee should be.
"The reason being is because in many people's eyes, whoever Jonathan chose to nominate would be an indication of whether Jonathan himself intends to run for the presidency in 2011.
"The nominee [Sambo] is perceived by many as one that will work with Jonathan and will not oppose his potential desire to run for president in 2011.
"[Sambo] may not be of the Nigerian elite, but he is a candidate from Nigeria's Muslim north, the same region the late Yar'Adua came from."