Sandusky was a longtime Paterno aide until he retired in 1999. He now faces 52 criminal counts for what prosecutors say was sexual abuse of 10 children over 15 years. He has denied the allegations.
Sandusky was Paterno's top assistant for years until he retired in 1999.
Paterno was fired Nov. 9 in the wake of the scandal and questions about his handling of the situation.
"He maintained a high standard in a very difficult profession. Joe preached toughness, hard work and clean competition," Sandusky said. "Most importantly, he had the courage to practice what he preached."
Two Penn State officials charged in connection with the sexual-abuse scandal also offered condolences.
Athletic director Tim Curley, who is on administrative leave, said in a statement issued through his attorney that "words cannot express" the sorrow he and his family feel.
"Joe has been an integral part of my life for more than 35 years," he said. "Joe coached me, mentored me, taught me what it meant to compete with integrity and honor, and above all demonstrated with each day that he lived, the power of humility. Our thoughts, prayers and sincere condolences go out to the Paterno family."
Retired vice president Gary Schultz said: "With profound sadness, my family and I want to express our heartfelt condolences for the Paterno family today. I had the sincere honor and distinct pleasure to work with Joe for many, many years at Penn State. No one loved Penn State more than Joe. We will all miss him."
Schultz and Curley await trial after pleading not guilty to charges of perjury and failing to report to authorities sex-abuse allegations against Sandusky in 2002.