The AP Player of the Year in 2009 made the largest donation ever from a Sooners basketball player to help with the $7 million center.
"I'm a little overwhelmed," Griffin said. "Having my family's name up there. ... It's something I'm very proud of."
The school's Board of Regents agreed to name the facility for Griffin, but he wanted his family included. Griffin said his brother, former Sooner Taylor Griffin, helped with the planning.
The facility includes basketball training courts, free weights and areas spaces for stretching, cardiovascular training and strength testing. There are locker rooms, an exam and recovery area and a fueling station.
The center, which is approximately 16,000 square feet, has been in use for the past two months.