The air and ground attack targeted a FARC camp near the town of Tame, in a rural area near the border with Venezuela, the military said.
During the operation, a helicopter was hit by rebel fire but was not brought down, a military statement said.
Besides the 14 FARC dead, whose bodies were recovered after the fighting, one rebel was wounded and another surrendered, it said.
The government of President Juan Manuel Santos has been in peace talks with the FARC since November 2012, but has vowed to keep up military pressure on the group until a comprehensive peace is reached.