US President Barack Obama: "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."
Former prime minister Tony Blair: "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."
Bill Gates, founder of rival company Microsoft and Mr Jobs's friend: "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."
Tim Cook, who replaced Mr Jobs as Apple chief executive: "Steve leaves behind a company that only he could have built, and his spirit will forever be the foundation of Apple."
BBC Director General Mark Thompson: "It's hard to think of anyone who changed our world more over the last 10 years."
Irish premier Enda Kenny: "Steve Jobs was a creative genius who broke down walls in business and opened doors in people's minds."
Ratan Tata, chairman of Tata Sons, the global business group: "Apple's products, under his leadership, have had a profound impact on mankind, unequalled by any other company in the information and technology space."
Facebook founder Mark Zuckerberg: "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."
David Clarke, chief executive of BCS, the Chartered Institute for IT: "His legacy is assured and his ideas are likely to shape the world for generations to come. He will undoubtedly be missed."
The following were taken from Twitter:
Simon Pegg, star of Shaun Of The Dead: "Very sad to hear about Steve Jobs. An innovator and trailblazer, whatever your tech tribe. Rest IP."
Radio 1 DJ Zane Lowe: "Steve Jobs RIP. A man whose exceptional vision helped to greatly sharpen ours."
Journalist and author Tony Parsons: "The death of Steve Jobs recalls the grateful sadness felt when John Lennon and Joe Strummer died. One dreaming man truly can change the world."
Writer and comedian Stephen Fry: "He changed the world. I knew him a little and admired him entirely."
Manchester City FC's Italian striker Mario Balotelli: "RIP Steve Jobs, your iPad got me through many boring benching sessions."
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."
BBC Radio 2 presenter Jeremy Vine described Mr Jobs as an "utter genius" and "officially irreplaceable".
Breakfast television presenter and Strictly Come Dancing contestant Dan Lobb: "I have a MacBook Pro, two iPods and an iPhone. Is my life more enhanced and more fun with them? A resounding yes! Sad to hear Steve Jobs has died."
Lord Sugar: "We started our computer biz at same time and were competitors thru 80's. Great visionary. Sadly missed RIP."
Comedian Patrick Kielty: "By now, Moses will have the Commandments on an iPad. RIP Steve Jobs."
In his own words: 'Find what you love'
No one wants to die. Even people who want to go to heaven don't want to die to get there. And yet death is the destination we all share. No one has ever escaped it. And that is as it should be, because Death is very likely the single best invention of Life. It is Life's change agent.
It clears out the old to make way for the new. Right now the new is you, but someday not too long from now, you will gradually become the old and be cleared away. Sorry to be so dramatic, but it is quite true.
Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma — which is living with the results of other people's thinking. Don't let the noise of others' opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition.
They somehow already know what you truly want to become. Everything else is secondary.
Mr Jobs helped to set up the company in 1976 after dropping out of college.
In October 2003 he was diagnosed with pancreatic cancer, although details emerged only the following year after he revealed he was to step back from the company to fight the disease after a special diet had failed to cure it.
Fears about his health resurfaced several years later, with commentators noting his gaunt features and weight loss.
In 2009, days after denying his ill health to shareholders, Mr Jobs revealed he was to take a leave of absence of six months. His exact issues were not disclosed, although it emerged his treatment had culminated in a liver transplant.
He returned to the company that summer and made his first public appearance in September of that year, as ebullient as ever about the company's products.
From Macintosh to the iPad
1976 Jobs co-founds Apple
1980 Apple's stock market flotation is biggest since Ford in 1956
1985 Leaves Apple to concentrate on new ventures, including Pixar and NeXT
1997 Returns to Apple promising to revitalise the flagging company
2000 Resumes as Apple CEO
2002 iPod launched
2003 iTunes launched
August 2004 announces he has been diagnosed with pancreatic cancer and has undergone surgery to remove tumour.
2007 iPhone launched
June 2009 Returns to work six months after taking time off for liver transplant as part of cancer treatment
January 2010 iPad launched
17 January 2011 Announces he is taking a break from day-to-day operations to concentrate on his health.
11 March 2011 iPad 2 launched
24 August 2011 Jobs resigns as Apple CEO
05 October 2011 iPhone 4S launched
06 October 2011 Apple announces the death of Steve Jobs