Apple's stock began a steady climb late last week and hit a new high of $664 (£422) a share during Monday trade on the Nasdaq (Nasdaq: ^NDX - news) exchange. It eventually closed even higher, at $665.15 (£423.48). It is now worth well over $620bn (£394bn).
The move upwards came amid rumours that the tech giant is poised to release new versions of its iPhone, iPad and Apple TV devices.
Its (Euronext: ALITS.NX - news) new market value - the price of its stock multiplied by the number of outstanding shares - eclipsed the previous record of $618.9bn (£394.1bn) set by Microsoft on December 30, 1999, at the height of the dot-com bubble.
Apple has actually been the world's most valuable company since the end of last year.
However, analysts point out that the comparison to Microsoft does not take inflation into account.
In inflation-adjusted dollars, the software giant was worth some $850bn (£541.2bn) on December 30, 1999.
It is now valued at £163.6bn.
Apart from the iPhone and mini iPad, analysts are speculating that Apple plans to make a TV set to complete its suite of consumer electronics products.
However, the company usually refuses to comment on its future product plans until a few weeks or days before a launch.
Apple's stock surge has made it a major part of many investment portfolios, often without the investors realising it.
The company makes up 4.7% of the value of the Standard & Poor's 500 index, which is used as the basis for many mutual funds.
China's largest oil company, PetroChina, could lay claim to having hit a market capitalization even higher than Apple's, because of the particularities of the Chinese stock market.
PetroChina was briefly worth $1trn (£636bn) on after it listed on the Shanghai exchange in 2007, but only based on its price on that exchange, which is isolated from the rest of the financial world because of Chinese laws on foreign investment.
PetroChina's shares also trade in Hong Kong and on the New York Stock Exchange, and based on prices there, its market capitalisation never went as high as $500bn (£318bn).