President Juan Manuel Santos and the top leader of Colombia’s biggest Marxist rebel group on Wednesday announced a breakthrough in peace negotiations that they say brings their country closer to ending a half-century of conflict.

“We are adversaries, but today we advance in the same direction, the most noble direction of any society, which is peace,” said Mr. Santos, speaking in the Cuban capital, Havana, where the talks have been taking place since November 2012.

Mr....