Starc's match-winning effort in Mackay, where he claimed 10 wickets and helped Australia crush Bangladesh in a two-day Test, has been rewarded with the No.1 spot on the ICC's charts.
It is the first time the left-armer has ever claimed top spot on the Test bowling rankings, which use a points system based on performances in recent years.
Starc was crowned player of the match and series after snaring 6-12 and 4-39 in the second-Test rout.
Indian pace ace Bumrah had held top spot on the Test bowling charts for two months.
Starc now sits 10th on the list of all-time Test wicket-takers with 445 scalps, having overtaken South Africa's Dale Steyn (439) on the standings with his haul in Mackay.
The 36-year-old told AAP ahead of Australia's two-Test series against Bangladesh that a clearer head and an ability to let things go were the secrets behind his remarkable form at an age when most fast bowlers have slowed down.
"You're never as good or bad as you think or other people think you are," Starc said.
"I still moan and whinge about anything that goes wrong or feels wrong. Even heading into (last) summer, it didn't feel like it clicked until the day before the Ashes.
"But I think what's been a feature of our group and led by 'Ron' (coach Andrew McDonald) and Pat (Cummins, Australia's captain), is that whether it's a good day, bad day, good over, bad spell, it's done. Move on.
"When you're 36 and you've been around for 16 years, you'd like to think you've improved or got better at something. You're also around that long because you're able to develop and learn and improve."
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