It comes a day after they were found guilty of terror charges at a trial in the capital N'Djamena.
Security sources said they were shot at a firing range north of the capital.
All 10 were convicted over their roles in twin attacks on the capital in June, which killed at least 38. A month after the attack, Chad reintroduced the death penalty for acts of terror.
"They were shot this morning at the Massaguet firing range," a source told Reuters news agency, referring to a city about 60km (40 miles) north-east of N'Djamena.
Among those to die was Mahamat Mustapha, aka Bana Fanaye, who had been described as the "mastermind" of June's attacks.
A school and a police building in the capital were targeted by suicide bombers on motorcycles, leaving more than 100 people injured in addition to the dead.
Those attacks were followed by a blast at a market in the capital in July, which killed 15 people.
The attacks were the first by the Nigerian-based group in Chad, which hosts the headquarters of a regional force set up to fight the militants.
The 10 were found guilty of charges including criminal conspiracy, killings, wilful destruction with explosives, fraud, illegal possessions of arms and ammunition, and using psychotropic substances, according to chief prosecutor Bruno Mahouli Louapambe, quoted in AFP news agency.
Chad has been instrumental in helping Nigeria retake most of the areas Boko Haram had seized.
The jihadists, who want to create their own Islamic caliphate in Nigeria, have killed thousands and forced millions to flee their homes in the country's north-east Nigeria since 2009.
The militant group had previously threatened to attack Chad, after it sent troops to help Nigeria recapture territory from them, mostly in Borno state.
Following the bombings, Chad banned people from wearing the full-face veil.
But its attempts to crack down on terrorism have attracted criticism from opposition and civil liberties groups who fear it could be used to curb civil rights.
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Ten members of the Islamist militant group Boko Haram have been executed by firing squad in Chad.