"Celebrating Steve on what would have been his 66th birthday," he wrote. "Especially in a year where so much kept us apart, technology brought us together in limitless ways. That's a testament to Steve's life and the legacy he left, which continue to inspire me every day."
Jobs, who co-founded Apple with Steve Wozniak and Ronald Wayne in 1976, died Oct. 5, 2011, after a battle with cancer. He was 56.
In a May 2010 commencement speech at Auburn University, Cook noted that Jobs was the one who convinced him to leave Compaq for Apple in 1998.
"No more than five minutes into my initial interview with Steve, I wanted to throw caution and logic to the wind and join Apple," he said. "My intuition already knew that joining Apple was a once-in-a-lifetime opportunity to work for the creative genius and to be on the executive team that could resurrect a great American company."