The 22-year-old, who averaged 9.4 points per game last season, would have been a restricted free agent had he not signed the deal before the October 31 deadline.
"We have tremendous respect for and confidence in Derrick and see him as an important part of our future. He brings a toughness and defensive mindset that make him a key piece to what we are trying to build here," general manager Dennis Lindsey said in a statement.
"Derrick is also a high-character individual and he has shown a dedication to continue to improve all aspects of his game."
Favors, a former Mr Basketball USA, joined Utah in 2011.