The pioneering former chief executive - who gave the world the revolutionary iPhone and iPad devices - died yesterday surrounded by his family after battling pancreatic cancer.
Fans gathered outside the 56-year-old's home in California's Silicon Valley today to pay their respects and lay floral tributes to a technology wizard who enjoyed a popularity equal to that of many rock stars.
Across the world the great and the good issued statements celebrating his life and applauding his achievements.
Bill Gates, founder of rival company Microsoft but also a friend of Mr Jobs, said he would miss him "immensely".
"The world rarely sees someone who has had the profound impact Steve has had, the effects of which will be felt for many generations to come," he added.
US President Barack Obama also applauded Mr Jobs, saying: "Steve was among the greatest of American innovators - brave enough to think differently, bold enough to believe he could change the world, and talented enough to do it.
"He transformed our lives, redefined entire industries, and achieved one of the rarest feats in human history: he changed the way each of us sees the world.
"The world has lost a visionary."
No longer able to handle the job because of his illness, the frail-looking father-of-four surrendered his chief executive post in August and was replaced by Tim Cook.
But he retained a leadership role as chairman of the company's board.
Mr Cook said Apple had "lost a visionary and creative genius".
In an email circulated to staff, he said: "Steve leaves behind a company that only he could have built, and his spirit will forever be the foundation of Apple.
"No words can adequately express our sadness at Steve's death or our gratitude for the opportunity to work with him.
"We will honour his memory by dedicating ourselves to continuing the work he loved so much."
In a career spanning more than 30 years, Mr Jobs changed the way the world thinks about technology.
Prime Minister David Cameron said: "Steve Jobs transformed the way we work and play; a creative genius who will be sorely missed. Our thoughts are with his family."
Facebook founder Mark Zuckerberg wrote on his Facebook page: "Steve, thank you for being a mentor and a friend. Thanks for showing that what you build can change the world. I will miss you."
Mr Jobs' family issued a statement saying: "Steve died peacefully surrounded by his family.
"In his public life, Steve was known as a visionary; in his private life, he cherished his family.
"We are thankful to the many people who have shared their wishes and prayers during the last year of Steve's illness.
"We know many of you will mourn with us, and we ask that you respect our privacy during our time of grief."
Mr Jobs started Apple Computer with school friend Steve Wozniak in his garage in 1976 but was forced out a decade later.
He returned in the mid-1990s and transformed Apple into one of the world's most powerful companies.
Customers didn't just hand money over for products - they became fans and devotees.
Mr Jobs, described by many as an industry oracle who revolutionised computing, survived pancreatic cancer in 2004 before receiving a liver transplant in 2009.
He had taken three spells of leave over the past few years, most recently in January.
After quitting Apple in 1985, Mr Jobs went on to co-found Pixar Animation Studios, which has created some of the most successful animated films of all time including Toy Story, A Bug's Life and Finding Nemo.
In 2006, he sold Pixar to The Walt Disney Company and secured a seat on the board.
He returned to Apple as an adviser in 1996 - the year it lost 900 million US dollars (£580 million) as Microsoft Windows-based PCs dominated the computer market.
However, the tide started to turn following the hugely successful 1998 release of the iMac and Mr Jobs later became chief executive.
Apple's popularity grew across the world throughout the past decade with the introduction of its sleek line of iPods, the iPhone and more recently the iPad.
Mr Jobs' starring role in the Apple story won him the adoration of fans from various backgrounds.
Ratan Tata, chairman of Tata Sons, the global business group, said: "Steve Jobs has been one of the greatest icons of the modern era.
"His untimely death is a huge loss to us all. His creativity, innovativeness and unbelievable attention to detail in every single area gave the world the early personal computer, the iPod, the iPhone and the iPad which have perhaps brought about the greatest change in the way people wirelessly listen to music, view visual images, exchange data and communicate."
Former prime minister Tony Blair described Mr Jobs as extraordinary.
He said: "As much as anyone in any walk of life in the early 21st century, he changed people's lives simply by imagination and determination. His memory will serve as a symbol of what the human mind can achieve."
Social networking websites were swamped as fans shared their thoughts.
Mr Jobs' achievements struck ordinary members of the public and celebrities alike.
Among tributes on Twitter, the writer and comedian Stephen Fry wrote: "He changed the world. I knew him a little and admired him entirely."
Referring to the improved, updated versions of iPhones, comedian David Baddiel joked: "If only God was more like Apple, and could bring him back as Steve Jobs 2S."
Lord Sugar remembered his Amstrad computer company competing with Mr Jobs in the 1980s.
He wrote: "Gutted: Steve Jobs died.
"We started our computer biz at same time and were competitors thru 80's. Great visionary. Sadly missed RIP."
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