Jobs was offered the post of CEO in July after Gil Amelio resigned, but said he was committed to his role as head of Pixar Animation Studios. However, Apple has been unable to replace Amelio and Jobs has been unofficially running Apple from the moment he stepped out through the door.
It may be difficult to find someone to replace Jobs. Apple has lost almost $2bn in the past two years, and Jobs has embarked on a controversial, high-risk strategy to try to save the company. Last month he announced a deal with Microsoft that boosted Apple's share price. This month he is being condemned for killing off the fledgling Mac "clone" industry.
For two years Apple has been licensing its Macintosh operating system to other companies to try to expand the Mac's market share. It signed deals with Motorola, IBM and Power Computing, hoping that they would start a whole new industry, just as PC clone companies did in the Eighties. But Apple found that the clone companies were simply cannibalising its own sales.
This month, Apple paid $100m to take over Power Computing, the most successful of these companies. And, last week, Motorola and IBM shut down their manufacturing operations after Apple refused to extend their licences to cover new hardware and software designs. "We had no choice," said Joe Guglielmi, vice-president of Motorola. "They invited us in, then shut us out."
This decision could have serious long-term repercussions for Apple, as Motorola produces the PowerPC chips that Apple uses inside all its computers. For now, Motorola says it will continue to supply Apple with chips, but any weakening of support from Motorola could leave Apple with nothing to put inside its computers.
Jobs's defence is that Apple had to end licensing in order "to restore Apple's financial health". His critics argue that the sales lost to clone manufacturers account for only a fraction of the billions of dollars that Apple has lost since 1995, and that Jobs is blaming the cloners for Apple's failures.
Jobs's actions may indeed help Apple's finances in the short-term. But Apple has isolated itself from its former allies and angered customers who benefited from the lower prices offered by the clone companies. The famous loyalty of Mac users seems to be close to breaking-point.
In a recent discussion, Jobs said: "I may not be perfect, but I'm the best hope you've got." He has asked for 90 days in which to reorganise Apple and "move forward to invent our future".
Meanwhile, will Jobs continue as full-time CEO? If not, Apple will have trouble finding a CEO who is prepared to take on a company that is so obviously under Jobs's control.
The difficulty of finding a successor to Jobs was underscored by the resignation of Apple's vice-president, Guerrino De Luca, less than 24 hours after Jobs was named as CEO last week. Another popular choice would be Apple board member Bill Campbell, but Campbell has also said that he is not interested in the job.
It may be that there's little point in speculating about who's going to run Apple. Much more important is the question of what kind of Apple will be left when Jobs has had his 90 days.