State television footage shown to officials and journalists showed jubilant police celebrating around the body.
Earlier a Reuters news agency reporter and other local journalists said that they had seen Yusuf in detention at a military barracks in Maiduguri and suffering from no visible injuries.
"There had been reports all over Nigeria that they had arrested him, that they had detained him and that he was killed in their custody," Al Jazeera's Yvonne Ndege, reporting from Maiduguri, said.
"They [the police] say this is total propaganda designed to discredit the Nigerian security services."
"They say that he was killed in a shootout in the compound where he lived, where they found explosive materials, a clinic making all sorts of chemical weapons, they say, and a room where they were putting together all sorts of police uniforms."
A correspondent for the UK-based BBC news network said a video shown to officials and journalists showed Yusuf confessing and saying he regretted his actions.
"The next moment on the video footage he was seen shot ... They showed his body," the correspondent said.
New York-based Human Rights Watch described Yusuf's death as "an extra-judicial killing".
"The extra-judicial killing of Mr Yusuf in police custody is a shocking example of the brazen contempt by the Nigerian police for the rule of law," Eric Guttschuss, the organisation's Nigeria researcher, said.
He urged the Nigerian authorities to investigate the circumstances of the killing.
Nigerian security forces had attacked a compound and mosque in Maiduguri after fighters from Boko Haram launched apparently co-ordinated attacks across four northern states.
The complex was shelled overnight into Thursday before security forces shot many of those attempting to flee, witnesses and sources said.
A reporter for the Associated Press news agency saw soldiers shoot their way into the mosque before opening fire on those inside.
Boko Haram, which means "Western education is prohibited" in the local Hausa dialect, has called for the enforcement of sharia even among non-Muslims.
Nigeria's 140 million people are nearly evenly divided between Christians, who dominate the south, and the primarily northern-based Muslims.
Islamic law was implemented in 12 northern states after Nigeria returned to civilian rule in 1999 following years of military rule.