"We are the ones that carried out the attack in Abuja," Shekau said in the 28-minute video obtained by AFP, referring to the deadliest attack ever in Nigeria's capital which targeted a bus station packed with morning commuters.
Seated with a kalashnikov resting on his left shoulder and dressed in military uniform, the insurgent commander spoke in both Arabic and the Hausa language that is dominant in northern Nigeria.
The message was delivered to AFP in a manner consistent with previous videos from Boko Haram.
The bombing at the Nyanya bus terminal on the outskirts of Abuja was the first major attack in the capital in two years.
Most of the insurgents' violence in recent months had been concentrated in the group's remote northeastern stronghold, where the military is waging an 11-month-old offensive.
The attack in Abuja underscored the serious threat the Islamists pose to Africa's most populous country and top economy.
Shekau indicated that Boko Haram has fighters based in the capital.
"We are in your city," he said, addressing Nigeria's President Goodluck Jonathan.
Shekau has been declared a global terrorist by the United States, which has put a USD 7 million bounty on his head.
Hours after the Abuja bombing, gunmen stormed a girls' school in the northeast and kidnapped 129 students, an attack also blamed on Boko Haram that has sparked global outrage.
Forty-four of the girls have escaped so far, according to officials, and the military has said it has launched a major search and rescue operation.