Citing the "cowardly and barbaric acts perpetrated by Boko Haram terrorists", which killed 33 people in N'Djamena on Monday, the military said that it had "carried out reprisal airstrikes on the terrorists' positions in Nigerian territory" on Wednesday.
Six Boko Haram bases were destroyed in the air raids, which caused "considerable human and material losses", the military said in a statement.
Chad would continue its "merciless" pursuit of the insurgents "so that no drop of Chadian blood spilt goes unpunished," the statement added.
Monday's attacks on the police headquarters and a police academy in N'Djamena were the first in the capital of the west African country, which has taken a lead role in a regional offensive against Boko Haram.
No group has claimed responsibility for the attacks but Chad and its allies immediately blamed the Nigeria-based insurgents, who have carried out several attacks recently.