Muhammadu Buhari also said his government would do "all it can" to rescue the missing Chibok schoolgirls and any other missing person still kidnapped by Boko Haram, as he was sworn in yesterday.
Mr Buhari also pledged to move the centre of operations to stop the extremist group much closer to where they predominantly operate in the northeast of the country, and conduct a study into their origins and sources of support once they are defeated, so similar groups do not rise up again.
A Muslim, Muhammadu Buhari beat the Christian former president Goodluck Jonathan in democratic elections in March, becoming the first opposition candidate to defeat an incumbent leader in Nigeria.
He said: "Having just a few minutes ago sworn on the Holy Book, I intend to keep my oath and serve as President to all Nigerians.
"I belong to everybody and I belong to nobody.
"The most immediate [problem] is Boko Haram's insurgency. Progress has been made in recent weeks by our security forces but victory cannot be achieved by basing the Command and Control Centre in Abuja [in Central Nigeria].
"The command centre will be relocated to Maiduguri [in northeast Nigeria] and remain until Boko Haram is completely subdued.
"But we cannot claim to have defeated Boko Haram without rescuing the Chibok girls and all other innocent persons held hostage by insurgents. This government will do all it can to rescue them alive.
"Boko Haram is a mindless, godless group who are as far away from Islam as one can think of.
"At the end of the hostilities when the group is subdued the Government intends to commission a sociological study to determine its origins, remote and immediate causes of the movement, its sponsors, the international connections to ensure that measures are taken to prevent a recurrence of this evil."
Muhammadu Buhari was previously a military leader who took power in a coup d'etat 1983 until 1985, when he himself was overthrown in a coup.
He unsuccessfully ran in democratic elections in 2003, 2007 and 2011 before winning in 2015.