Starc was the leading wicket taker in the recently concluded series in South Africa, picking up 15 wickets in three tests.
Although Australia lost the final test to lose a thrilling series 2-1, Starc finished with nine wickets in the match which included a first-innings haul of 6-72.
Jansen had claimed the top position in the bowlers' and all-rounders' rankings only last week after a superb performance with the bat and ball in the second test, before being displaced by the 36-year-old Australian.
South Africa's Simon Harmer, who was named Player of the Match after the spinner claimed his maiden 10-wicket match haul in the third test, climbed nine places to seventh.