In early trading, the shares were down 2.5% before closing down 0.66% at $373.69.
Mr Jobs, who has been on medical leave since 17 January, will stay on as Apple chairman. The new boss will be Tim Cook, formerly chief operating officer.
Analysts suggested that the share price had not fallen further as investors had confidence in Mr Cook and his team.
“In our view, Tim [Cook] is a tough but well-regarded leader who will continue to hold Apple employees to an extremely high standard of performance,” said Richard Gardner at Citigroup.
Mr Cook, 50, has already been in charge of the company’s day-to-day running since January and took the helm in 2004 as Mr Jobs battled cancer and again in 2009 when Apple’s co-founder received a liver transplant.
He is credited with ensuring the efficiency of the firm’s supply chain and delivering Apple’s industry-beating profit margins.
No man is irreplaceable, and Apple is packed with brilliant engineers, designers and managers. The question now is whether it can continue to “think different” without the man who made that into a personal and professional credo.”
Terry Connelly, dean of the Ageno School of Business at Golden Gate University in San Francisco, said: “A company is dependent on its ability to institutionalise… genius in the corporate DNA.
“Apple shows every sign of having done that. We will see that when we see how Cook responds to competitive pressure.”
Van Baker, an analyst at Gartner, said there was no reason for investors to panic.
“Apple will do just fine,” he said. “There are so many talented people there, and Steve’s attention to detail is baked into the culture.”
Brand research company Millward Brown said the Apple brand should remain unaffected.
“[Steve Jobs] has left the Apple brand in rude health so that the company is still poised for future growth,” said Millward Brown director Peter Walshe.
He added that Mr Jobs had left Apple with a clear direction ahead, a successor in place, and a unique “creative”, “fun” and “adventurous” brand behind him.
Looking ahead, Ben Wood, research director at technology analysts CCS Insight said Tim Cook had a huge pair of shoes to fill, adding: “Steve Jobs has been a tremendous leader but no man is bigger than the company itself.”
Earlier this month, Apple was briefly the world’s most valuable by market capitalisation, overtaking oil company Exxon Mobil.
In his resignation letter, Mr Jobs said: “I believe Apple’s brightest and most innovative days are ahead of it. And I look forward to watching and contributing to its success in a new role.”
The company has some big products on the horizon such as the iPhone 5 and the iPad 3.
“Steve is [still] going to be able to provide the input he would do as a chief executive,” said Colin Gillis at BGC Financial.
“But Tim has been de facto chief executive for some time and the company has been hugely successful. The vision and the roadmap is intact.”
Stephen Fry, a long time admirer of Mr Jobs, told BBC News, “I don’t think there is another human being on the planet who has been more influential in the last 30 years on the way culture has developed.”
“If I had said that 10 years ago you’d have thought I was completely insane.”
One former employee, Dan Crow, who worked at Apple for four years, said staff at the firm would be feeling “very sad” and a “sense of loss”.
But he said the firm had “a whole suite of people who will replace most, if not all, of what Steve brought to the company”.
Mr Cook’s well-regarded team includes marketing chief Philip Schiller, design overseer Jonathan Ive, and Scott Forstall, who supervises the iPhone software.
Steve Jobs was famous for his charismatic presentation of new products, dressed in his trademark turtle neck and jeans.
Marketing chief Philip Schiller has fronted some recent presentations in Mr Jobs’ absence and he may continue to do so, rather than new chief executive Tim Cook, the BBC’s technology correspondent Rory Cellan-Jones says.