"I hope that today everyone will reflect on his extraordinary life and the many ways he made the world a better place," Cook, who took over for Jobs Aug. 24, 2011, wrote in a letter that appears after the video. "One of the greatest gifts Steve gave to the world is Apple."
The emotional, 90-second video features black-and-white photos of Jobs accompanied by some of his most notable quotes.
Jobs passed away from cancer last year at the age of 56.
Apple has gone on to become the most valuable company in the world.
"I'm incredibly proud of the work we are doing, delivering products that our customers love and dreaming up new ones that will delight them down the road. It's a wonderful tribute to Steve's memory and everything he stood for," Cook's letter ends.