It comes just two days after the Colombian government and the FARC resumed talks following months of stagnation at the negotiating table and fighting on the battlefield.
The talks designed to end the 50-year conflict -- Latin America's oldest insurgency -- have been dragging on since November 2012.
"I have issued the order to stop as of today bombing raids against camps where there are members of that group," Santos said in an address at a navy event in the northern city of Cartagena.
Santos similarly suspended the bombing campaign in March but ordered a resumption a month later after the guerrillas allegedly killed 11 soldiers.
The Revolutionary Armed Forces of Colombia (FARC) have been observing a unilateral, one-month ceasefire since Monday, but Santos had initially refused to reciprocate.
The latest efforts at speeding up the fragile peace process come after the conflict heated up once more in the spring, with dozens killed on both sides and many Colombians increasingly disillusioned with the pace of talks.
Bogota agreed for the first time to reduce its anti-rebel operations, a significant step in the talks in the Cuban capital Havana.
Nevertheless, sporadic clashes have continued.
Jorge Restrepo, director of the Conflict Analysis Resource Center (CERAC), told AFP that the president's order was a significant one.
"It's undoubtedly a breakthrough in the peace process," he said, adding that there had been a "substantial reduction" in violence since the FARC ceasefire.
The war in Colombia has left an estimated 220,000 dead and forced more than six million people from their homes.
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