"I couldn't be happier," Schieffer said. "Face the Nation is going to be in good hands."
Schieffer, who has hosted Face the Nation for 24 years, said last Wednesday that he would retire this summer.
"You know, I'm one of the luckiest people in the world because as a little boy, as a young reporter, I always wanted to be a journalist, and I got to do that," Schieffer said of his retirement. "And not many people get to do that, and I couldn't have asked for a better life or something that was more fun and more fulfilling."
Dickerson is already CBS News' political director and Slate magazine's chief political correspondent.
"I'm thrilled," Dickerson said. "I have watched Bob my whole professional life not just as a viewer but as a daily reporter who also covered the Hill. I'm honored to carry on his tradition on Face the Nation."