Geschke set up Adobe in 1982, giving the world the ubiquitous PDF software, among many other audio-visual innovations.
He made headlines 10 years later when he was kidnapped at gunpoint and held for ransom before being released unhurt after a four-day ordeal.
Geschke died in California on Friday.
Adobe CEO Shantanu Narayen said Geschke, widely known as Chuck, "sparked the desktop publishing revolution".
"This is a huge loss for the entire Adobe community and the technology industry, for whom he has been a guide and hero for decades," he wrote in an email to the company's employees.
"As co-founders of Adobe, Chuck and John Warnock developed ground-breaking software that has revolutionized how people create and communicate," he said.
Geschke and Warnock were responsible for transformative software inventions, including PDF, Acrobat, Illustrator, Premiere Pro and Photoshop, Mr Narayen said.
In 1992, Geschke was kidnapped in an incident that made national headlines.
He was held at gunpoint in his office and taken to Hollister, California, for four days.
Geschke was freed after a suspect, found with $650,000 (£470,000) in ransom money, took police to the location where he was being held, Associated Press reported.