During the day, the share price of the iPhone maker jumped by 2.8% to $207.05, passing the $1tn (£762bn) mark in NY trading.
Cook's hiring may have been one of the best things Jobs did for Apple.
Like the four-minute mile or breaking the sound barrier, the idea of a company with a market capitalization - the share price multiplied by the number of outstanding shares - of more than a trillion dollars was once nearly unthinkable. That also means the actual number of Apple shares may have fallen further since July 20, but most market observers go with the number reported in the 10-Q quarterly financial reports filed with the SEC.
Apple was founded in a Silicon Valley garage by college dropouts Steve Jobs and Steve Wozniak and their friend Ronald Wayne in 1976.
Apple was famously led for years by its visionary co-founder Steve Jobs.
The race to a $1 trillion market cap - symbolic as it is - has been closely watched on Wall Street.
Jobs often presented almost the entirety of Apple's launch events, while Cook typically emcees, but hands product announcements to lieutenants like marketing head Phil Schiller, software chief Craig Federighi, and services lead Eddy Cue.
Apple is the first private sector company to reach this level.
Tesla stock surges as Musk looks to make good with analysts
We're speaking of Pole Position , and if Musk gets his way you'll be able to play the game using the Tesla's own steering wheel. The company's cash reserves have dropped to $2.2 billion, down from $3.3 billion at the end of previous year .
Cook has leveraged the legacy that Jobs left behind to stunning heights.
Apple has what is considered the most devoted brand community in the world and its ad campaigns are legendary for personal touches that foster a deep loyalty among its customers.
"It didn't just change Apple, it changed the whole computer industry", Jobs said of the Macintosh in 2007. Since then 18 different iPhones have been launched and more than 1.2bn of the devices have been sold. "This trinity established Steve's vision and created the Apple we know today".
Apple came of age of age at such a speed that it surpassed a giant like Exxon, which is still a very profitable oil company. Cisco stock rose 1.6 percent on the news.
A Forrester analyst said of the company, "Whether they stand alone or are acquired, Apple as we know it is cooked".
Apple took advantage of that break to bring back virtually all of its overseas cash, triggering a $38 billion tax bill.
In a US regulatory filing this week, Cook warned tariffs being imposed in a US-China trade war could result in Apple paying more to make its products, eating into profit or forcing up prices for consumers.