The targets of the bombardment included the town of Gwoza, where Boko Haram leader Abubakar Shekau first proclaimed the existence of a caliphate inside in Nigeria in August, and the notorious Sambisa Forest area, where the rebels have had camps for years.
"The air strikes which today targeted... Sambisa forests and parts of Gwoza have been highly successful," defence spokesman Chris Olukolade said in a statement.
"The death of a large number of terrorists has been recorded."
The Sambisa Forest is believed to be the area where more than 200 schoolgirls kidnapped by Boko Haram in April were taken before being divided into groups and moved.
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The Islamist militants took over Gwoza in July and tried to encourage people to stay and live under the group's so-called caliphate.
The current population of the town is not known and it was not clear if any civilians were killed in the air force bombardment.
But the regional militaries have offered different accounts of operations so far.
Chad this week said its fighters were advancing towards Sambisa Forest after crossing the border and overpowering the Islamists in the Borno town of Dikwa, 50 kilometres from their base on the Cameroon border.
Nigeria has insisted its military is leading the operation, which aimed at containing the insurgency which has killed 13,000 people since 2009.