"We are the strongest team in the group. We are not afraid of confronting Ghana," Bradley said at the draw.
Ghana was the best-performing African team at the last World Cup, when it beat the Bradley-led United States in the second round, and will be at home in the first leg. Authorities haven't yet decided if fans will be allowed in to the second leg in Egypt, where recent national team games have been held behind closed doors and in the Red Sea resort of El Gouna, away from the country's unsettled major cities.
Ivory Coast was pitted against Senegal about a year after a riot at a stadium in Dakar when they met in African Cup qualifying. Ivory Coast will be at home first. Senegal reached the World Cup quarterfinals in 2002, only the third African country to achieve that feat, but hasn't appeared on the biggest stage since then.
Ethiopia emerged from a long spell of underperforming to play at the African Cup of Nations this year, but faces a tough draw against new African champion Nigeria. Ethiopia hosts the first leg.
Tunisia was given a second chance at the World Cup after Cape Verde forfeited its victory over the Tunisians in the final round of group games and was thrown out the playoffs for playing Fernando Varela when he should have been suspended. Tunisia will be led by interim coach Ruud Krol after Nabil Maaloul quit in disgust at the 2-0 home loss to Cape Verde days before Tunisia was reinstated by FIFA.
"It is a chance for redemption for the Tunisian players," said Youssef Zouaoui, Tunisia's technical director of national teams.
Tunisia will host Cameroon first, which will be without all-time leading scorer Samuel Eto'o for the playoffs after the Chelsea striker retired from the national team.
Burkina Faso surprisingly reached the final of the African Cup this year, while Algeria, ranked No. 3 in Africa behind Ivory Coast and Ghana, is seeking successive appearances at World Cups.
"We avoided teams like Senegal, Cameroon and above all Egypt, but we must not get cocky, it will be 50-50," Algeria coach Vahid Halilhodzic said on national radio.
Burkina Faso hosts the first leg before the underdog Burkinabes chase their place in history away in Algeria.
"We believe playing the second leg away from home could be advantageous with our opponent feeling a lot pressure at home," Burkinabe Football Federation president Sita Sangare said.