The 10 men were sentenced to death on Friday after being convicted of crimes including murder and the use of explosives. They were killed at around 11 a.m., Ahmat Mahamat Bachir, the security minister, said.
Those killed included Bahna Fanaye, alias Mahamat Moustapha, who Chadian officials have described as a leader of the Nigeria-based group.
Chad has vowed to take a leading role in a regional force to fight Boko Haram that is also expected to include soldiers from Cameroon, Benin and Niger in addition to Nigeria.
Boko Haram has targeted Nigeria’s neighbours in regular attacks this year.
In June and July Chad’s capital, N’Djamena, was rocked by a series of suicide attacks that killed dozens of people — the first such attacks since Boko Haram threatened the country earlier this year.
In one attack, suicide bombers on motorcycles targeted two buildings in the capital. In another, a man disguised as a woman wearing a burqa detonated a bomb outside the city’s main market.
Last September, Chad drew praise from rights groups for a draft penal code that abolished capital punishment. The International Federation for Human Rights said at the time that the country had observed a moratorium on the death penalty since 1991 with the exception of nine executions that took place in November 2003. But anti-terror measures approved by lawmakers last month in response to the recent attacks brought the death penalty back.