The announcement was made at the annual Black Hat conference in Las Vegas.
Apple head of security engineering and architecture, Ivan Ksrtic, said the programme would be open to 24 handpicked researchers at the start, but others who submitted bug reports in any of five classifications could also be eligible for rewards.
For bugs in secure boot firmware components, the reward will be US$200,000. Bugs relating to the extraction of confidential material protected by the secure enclave processor will net US$100,000.
The chosen researchers can look for bugs in both iOS and iCloud.
Ksrtic was quoted as saying: "We've had great help from researchers like you in improving iOS security all along. As the mechanisms we build get stronger, the feedback I've gotten from my team is that it’s getting increasingly difficult to find those vulnerabilities.
"The Apple bounty programme will reward researchers who share critical vulnerabilities with Apple and we will make it a top priority to resolve those and provide public recognition."