Smith started Australia's tour of the West Indies at No.4 but has now leapfrogged the previous No. 1, Kumar Sangakkara, as well as AB de Villiers and Hashim Amla, to take the top spot.
Smith was Man of the Match in Australia's victory in the second Test in Kingston, where he made 199 in the first innings, and it continued a remarkable period: he is Test cricket's leading run scorer over the past year, with 1226 at 102.16.
The series in the Caribbean also marked the first time he had moved up to No.3 in Australia's Test batting order.
Sangakkara had been at No. 1 since January this year, when he replaced de Villiers, who in turned had reclaimed the top position from Sangakkara the previous month.