Martin, the former quarterback who led Tennessee to the 1998 national title, is in his first season on Trojans coach Lane Kiffin's staff.
"I was very honored to be offered a position on Coach Jones' Tennessee staff," Martin said in a statement posted on school's website. "I truly believe he will do an outstanding job with the Vols program. My decision to remain at USC was the toughest I have ever had to make because Tennessee is such a special place to me.
"At the end of the day, I am a man of my word. I promised Coach Kiffin when I was hired at USC that I had goals I wanted to accomplish here. We still have work to do here to reach those goals. I see a great future at USC with the players on our roster and the recruits we have coming in.
"I have so much love and respect for Tennessee. But at this time, the right decision was to continue at USC and I am looking forward to doing that."