Smith has been at the top for 167 Tests played worldwide in total.
He takes over from New Zealand captain Kane Williamson, who is set to lead his team in the ICC World Test Championship Final against India at the Hampshire Bowl in Southampton from Friday.
Williamson, who scored 13 runs in the first Test against England, had missed the second Test due to elbow problems, slipped five points behind Smith’s 891 rating points, and is second on the batters’ list.
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This means that Smith has been at the top for 167 Tests played worldwide in total, only behind Garry Sobers (189 matches) and Viv Richards (179 matches).
This week’s update also included performances from the first Test between South Africa and the West Indies in St Lucia and sees Quinton de Kock in joint-12th position with Cheteshwar Pujara while his compatriot Adrian Markram has advanced two slots to reach 14th position.
De Kock scored 141 and was named Player of the Match as South Africa won the Test by an innings and 63 runs.
Kagiso Rabada has gained two spots to reach the seventh place after a five-wicket haul in the second innings, Anrich Nortje is up into the top 30 for the first time in his career finishing with seven wickets in the match, while Lungi Ngidi is up 14 places.
(ICC inputs)