He did not say what had happened to Abubakar Shekau, but said he had been replaced by Mahamat Daoud – who has not been heard of before.
Mr Shekau has not featured in the group’s recent videos, leading to speculation that he has been killed.
Mr Deby, whose troops have been involved in battling Boko Haram, said Mr Daoud was open to dialogue.
The BBC’s Nigeria correspondent Will Ross says that last year, the Chadian leader was said to be brokering peace talks with Boko Haram.
But the negotiations never happened and were widely seen as a sham so some analysts will question how much credence to give to Mr Deby’s latest comments about the jihadist group, he adds.
Mr Shekau took over as the group’s leader after the its founder, Muhammad Yusuf, died in Nigerian police custody in July 2009.
Under his leadership the group has become more radical and carried out more killings.
The last Boko Haram video, which was released earlier this month, showed an unidentified young man speaking in the name of the Islamic State in West Africa calling on people to be patient: “We are still present everywhere we had been before.”
He spoke in the regional Hausa language, with an accent from the Kanuri ethnic group, to which Mr Shekau belongs.
In numerous videos, Mr Shekau has taunted the Nigerian authorities, celebrating the group’s violent acts including the abduction of the more than 200 Chibok schoolgirls in April 2014.
He was last heard from in March, when he released an audio message pledging allegiance to the Islamic State (IS) group.
Last month, Nigeria’s new President Muhammadu Buhari said he would be willing to negotiate with the Boko Haram leadership for the release of the Chibok girls – depending on the credibility of those saying they represented the group.
A previous prisoner-swap attempt ended in failure.
Earlier this year, Chadian troops played a key role in a regional effort to retake towns and villages held in north-eastern Nigerian by Boko Haram.