The Colombian military killed Reyes in an air raid on Saturday in neighbouring Ecuador, dealing a major blow to the group, officials said earlier in Bogota.
Ecuador protest
Rafael Correa, Ecuador's president, has said he will send a diplomatic note to protest the Colombian military incursion.
Colombian ground troops were then deployed into the Farc hideout to secure the area, Santos said. A total of 17 rebels and one soldier were killed in the operation.
"It is the heaviest blow ever dealt against this terrorist group," Santos said.
Reyes, 59, whose real name was Luis Edgar Devia, was a union leader working for Swiss food giant Nestle in the southern department of Caqueta when he joined the Revolutionary Armed Forces of Colombia (Farc) in the 1970s.
The grey-bearded, bespectacled rebel, who went on to become the Farc's chief spokesman, donning olive fatigues and carrying a rifle, had been viewed as a possible successor to the group's 77-year-old boss, Manuel Marulanda.
His killing was a major coup for conservative President Uribe, who has taken a hard stance against the 17,000-strong Farc, South America's biggest insurgency which has bedeviled successive governments since the 1960s.
It was the first time that one of the seven members of Farc's secretariat, or leadership council, was killed in combat.