Apple CEO Steve Jobs has left the building. The 56-year-old Jobs resigned late yesterday.  In a letter of resignation published to Apple’s website, Jobs said he had urged the company’s board of directors to appoint Apple COO Tim Cook as his successor. Apple has confirmed Cook as the company’s new CEO.

Jobs, who is in the midst of a long bout with pancreatic cancer, is currently on medical leave. While he made no specific mention of his condition in his letter of resignation, Jobs did reference his ability to fulfill his duties at Apple.

“I have always said if there ever came a day when I could no longer meet my duties and expectations as Apple’s CEO, I would be the first to let you know. Unfortunately, that day has come,” Jobs wrote.

While he won’t be involved in day-to-day operations, Jobs said he would like remain on as chairman of the board, director and Apple employee, given the board’s approval.

Over the years Jobs has become as iconic a presence at Apple as the devices the company produces. He started Apple Computer back in 1976 but was forced out by the company’s board of director a decade later. In a 2005 commencement speech delivered at Stanford, Jobs called this one of the most profound events of his life.

“I didn’t see it then, but it turned out that getting fired from Apple was the best thing that could have ever happened to me,” Jobs said in the speech. “The heaviness of being successful was replaced by the lightness of being a beginner again, less sure about everything. It freed me to enter one of the most creative periods of my life.”

Jobs founded NeXT during that time, which was subsequently acquired by a floundering Apple in 1996. A year later, Jobs was reinstated as Apple’s CEO, and in 2001 he introduced the first iPod, the device that revolutionized the music industry. The rest, as they say, is history.

In 2004, Jobs took his first medical leave, undergoing a liver transplant in his absence, after a diagnosis of pancreatic cancer. Since then, Apple stock has fluctuated dramatically on news of the CEO’s health.

Roger Entner, founder of Recon Analytics, said that Jobs’ departure has been hanging over the company’s stock price for a long time.

“A company that’s executing so well and dominating in so many areas is trailing the market in terms of valuation. It’s mind blowing. Which means there was already this overhang of what happens if Jobs is leaving. Bottom line, the company shouldn’t trade as low as it does,” Enter said.

But Entner also said that regardless of what Apple stock does, Jobs’ departure shouldn’t have much impact on day-to-day operations or the rollout of new products in the short- to medium-term.

“Their product pipeline is stacked, and Steve hasn’t been there on a day-to-day basis since January. Tim Cook has been running the company’s daily operations since the first medical leave,” Enter said, adding that the company’s long-term success is entirely dependent on whether jobs has been able to imbue his existing people with his own vision.

“It remains to be seen how well Steve has passed on his really transformational vision into the people, and if they have that same vision, that same commitment to excellence that Steve displayed over the course of his career,” Enter said.

While many expected Apple’s stock to plunge immediately following yesterday’s announcement, it remained relatively stable in early morning trading. As of this writing, sharesof the company were down just 1.7 percent to $366, a far cry from the dive some analysts predicted.

Craig Cartier, analyst for the Information & Communication Technologies practice at Frost & Sullivan, said he’s not too worried about the impact on Apple, noting that Tim Cook has headed the company during each of Jobs’ medical leaves dating back to 2004 and will continue to be a capable leader in Job’ absence. Cartier also notes that Jobs is still around.

“When he stepped down as CEO in 2004 and again in 2009, Jobs stated that he would remain involved in major strategic decisions,” Cartier said. “Although today’s announcement is more long-term in nature, his strategic influence will remain through his new position as chairman of the board.”

News of Jobs departure comes as the company is expected to launch a new iPhone in the next couple of months. Rumors abound this week on the launch, with one report from the Wall Street Journal claiming that Sprint is in line to begin selling Apple’s iconic device by October.

Rumors aside, the next time Apple holds one of its high-profile product launches, Jobs will likely not be running the PowerPoint. Investors, Apple lovers and the rest are undoubtedly hoping that Jobs’ decision to resign was done with his own words in mind.

“You have to trust in something,” Jobs said back in that Stanford commencement speech, “your gut, destiny, life, karma, whatever. This approach has never let me down, and it has made all the difference in my life.”