Another 101 people were wounded in the simultaneous bombings outside the police headquarters and police academy in the capital N'Djamena, according to a government statement read on national radio.
It said four "terrorists" were also killed but did not give details. Earlier, a police official had said two suicide bombers carried out the attacks.
They were the first such bombings in the capital of the north-central African nation, where security has been beefed up since Chad joined the fight against Boko Haram earlier this year.
The government statement said the "situation is under control".
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Large numbers of Chad's security forces were seen taking up positions on the streets of the capital after the attacks.
President Idriss Deby was expected to return home during the day from an African Union summit in Johannesburg, an official said.
The former French colony is part of a four-nation coalition also including Nigeria, Cameroon and Niger that was created to tackle the Boko Haram insurgency as the group steps up cross-border attacks.
Paris condemned Monday's blasts, with a foreign ministry spokesman saying France "stands alongside Chad and its partners in the fight against terrorism".
Chad also is a close ally of France in its counter-terrorism Operation Barkhane in five countries in the Sahel region and the French army has set up its headquarters for the campaign in N'Djamena.
Last week, Abuja hosted a summit where Nigeria and fellow coalition members plus Benin rubber-stamped an 8,700-strong regional force to replace the current four-nation grouping.
Boko Haram has been waging a six-year campaign of violence in northeastern Nigeria that has left at least 15,000 people dead and increasingly spilled across borders.