Apple's stock market value is greater than the combined capitalisation of Exxon Mobil, Procter & Gamble and AT&T.
The company's stock was at $205.98, up 2.2 percent near 1555 GMT.
The company's fortunes were turbocharged by the launch of personal gadgets such as the iPod in 2001 and the iPhone in 2007.
Stock market veterans note that the first trillion-dollar public company - if only briefly - appears to have been PetroChina Co.
The ailing Jobs handed the corporate reins to his chief lieutenant, Cook, in 2011.
The milestone comes a day after Apple reported blockbuster quarterly earnings. His ignominious departure came after losing a power struggle with John Sculley, a former Pepsico executive who he recruited to become Apple's CEO in 1983 - seven years after he and his geeky friend Steve Wozniak teamed up to start the company with the administrative help of Ronald Wayne. Recently, some of his older clients have bought Apple shares for their grandchildren.
Bullish investors have rallied after the company's results for the June 30 quarter that handily beat Wall Street forecasts and its upbeat guidance for the September quarter with refreshed products expected this fall.
The rise is even more astonishing - 50,000% - since the company first listed in 1980. Also propelling Apple higher in recent months was Apple's announcement that it earmarked US$100 billion for a new share repurchase programme.
What makes it impressive is that Apple buys back a lot of its stock.