Santos told a news conference that the military operation had left a total of 17 rebels and one soldier dead.
He said that the Colombian Air Force did not violate Ecuadoran air space during the operation and that it was a well planned attack.
"Once the camp was bombarded, Colombian forces were ordered in to secure the area and neutralize the enemy."
"Colombian police was also asked to secure the area with the army, until Ecuadoran authorities arrived." Santos said:
Reyes' death is the latest in a string of killings by Colombia's armed forces against the rebels over the past few years.
The United States has always backed Colombia in its efforts to weed out the rebels.
The Colombian government had long accused the Farc rebels as "narco-terrorists" who funded their insurgency operations through cocaine trafficking and had held around 750 people hostage.
Reyes was Farc's chief spokesperson and the top contender to take over the reigns of Farc, from Manuel Marulanda, the group's founder.
He was also one of the six key members of Farc's secretariat.