Cricket South Africa named Amla on Tuesday ahead of wicketkeeper-batsman AB de Villiers, who appeared to be the front-runner to replace Smith.
The 31-year-old Amla has previously shied away from the captaincy role when approached to do the job in limited-overs cricket but had a change of heart after Smith's retirement.
Amla said in a statement: "I have concentrated on taking my batting to the highest possible level and now I feel I am in a position to make a contribution to South African cricket in a leadership role."
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