Jobs died at the age of 56 on Wednesday, October 5 after losing his struggle with pancreatic cancer.
Gates wrote on his personal website: "I'm truly saddened to learn of Steve Jobs' death. [My wife] Melinda and I extend our sincere condolences to his family and friends, and to everyone Steve has touched through his work.
"Steve and I first met nearly 30 years ago, and have been colleagues, competitors and friends over the course of more than half our lives."
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He added: "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.
"For those of us lucky enough to get to work with him, it's been an insanely great honour. I will miss Steve immensely."
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Watch Bill Gates and Steve Jobs appear together at All Things Digital 5 below: