Mr Jobs died in 2011 and was succeeded as chief executive by Tim Cook.
Apple has become the first publicly traded company to be worth $1 trillion. It became the first $900 billion company exactly nine months ago, on November 3, 2017.
The share price surge is credited to recent quarterly financial results that surprised investors on Wall Street for being better than expected.
Apple saw excellent numbers during its fiscal third quarter of the year, revealing strong worldwide sales and demand for the pricey iPhone X, which helped tip revenues to a new record despite a dip in device sales.
Apple, the company Steve Jobs and Steve Wozniak founded in 1976 in possibly not a garage, became the most valuable company in the world in 2012, passing Microsoft as iPhone sales pushed the company into the stratosphere.
Growth is coming from different sources, too, notably iPhone price increases and sales of ancillary products. The company's various services such as Apple Music, iCloud and Apple Pay now represent $9.6 billion in revenue.
Shares of the company rose 3% Thursday, and are up about 31% over the past year.More news: Pompeo announces new United States investments in Indo-Pacific region
Apple's stock has risen over 30 percent in the past year, fueled by optimism about the iPhone X, launched a decade after the original.
Elsewhere, Saudi Aramco, the state-owned oil company of Saudi Arabia, has reportedly been eyeing a public offering that could value it near $2 trillion, but a potential listing has been mired in delays.
"These are the actual shares outstanding able to trade, even though some may be held by insiders, interlocks or others", Silverblatt said. On Thursday, it was worth about $875 billion while Google's parent company Alphabet was worth about $850 billion.
The chart below shows the value over time of a $1,000 investment in Apple made at its December 12, 1980 closing price.
Apple faced another crisis when Jobs died in 2011 and investors anxious the company couldn't thrive without his intense, hands-on product-design leadership.
Last month, an ex-Apple engineer was charged in California with stealing trade secrets from a hush-hush self-driving auto technology project days before he quit to go to a Chinese start-up. Apple announced $100 billion in stock buybacks on May 1, the largest repurchase ever by a US public company. The value of Microsoft is also more than $800 billion.