Deby — in power for more than two decades in the oil-rich landlocked African state — has insisted the changes are necessary.
The measures establish a full presidential regime without prime minister or vice president and were passed by lawmakers on Monday.
The head of state is due to sign them into law on Friday.
A statement read on national television on Thursday announced Prime Minister Albert Pahimi Padacke and his government had stepped aside.
The constitutional changes comes despite opposition warnings that it would undermine democracy.
An appeal for the annulment of the bill, tabled Wednesday by 26 lawmakers of the Chadian opposition, was rejected Thursday after being heard by the constitutional court.
The changes will increase presidential terms to six years with a limit of two terms. The current mandate is five years with no limits on re-election.
The vote comes amid growing political tensions in Chad, ranked by Transparency International as one of the world’s most corrupt nations, as opposition groups boycotted a forum last month discussing the proposed changes.
Download our app and read this and other great stories on the move. Available for Android and iOS.