Olamikan Gbemiga/AP
A Nigerian soldier, center, walks, at the scene of an explosion in Abuja, Nigeria, that had been carried out by Boko Haram.
The Nigerian government and military officials were not immediately available to comment.
"Our troops entered Nigeria this morning. The combat is ongoing," one of the sources at Chad's army headquarters told Reuters.
Chad has deployed some 2,500 troops as part of a regional effort to take on the militant group that has waged a bloody insurgency to create an Islamist emirate in northern Nigeria. And its army has proven more effective than Nigeria's in fighting the jihadist group.
As the Wall Street Journal reported last month, Chad has sent a contingent of soldiers to Cameroon to help prevent Boko Haram's infiltration of that country. The group's push into the shoreline of Lake Chad, culminating in a massacre in the lakeside town of Baga last month that may have been Boko Haram's deadliest atrocity to date, convinced both Cameroon and Chad to step up their efforts along their porous borders with Nigeria.
The Nigerian military has had a spotty record fighting Boko Haram, taking a heavy-handed approach at some points while fleeing key towns at others. In contrast, the Chadian military has a recent record of success fighting jihadist groups. The country cooperated in successful French-led efforts in 2013 to remove jihadist militants that had seized the northern half of Mali, and the country's military helped free scores of Boko Haram hostages last August.