Martin returned Tuesday to Los Angeles, where he is a receivers coach at Southern California under former UT coach Lane Kiffin.
"I was very honored to be offered a position on Coach Jones' Tennessee staff," Martin said in a statement released by the school. "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."
Martin and his family caught a flight out of Knoxville on Tuesday morning, ending a one-day visit to the university he led to a national title in 1998 and a campus that has a street named in his honor.
Martin's rejection leaves Jones with one opening
still available on his on-field coaching staff. He could turn to his wide receivers coach at Cincinnati T.J. Weist, or seek other candidates in the South.
Martin arrived Monday with his wife and two children and spent the day visiting with Jones and his staff and touring UT's facilities.
"Things went really good," Martin said Monday night. "I had an opportunity to meet the staff and see everything that's changed (on campus). I could tell they were headed in the right direction."
"It's about making this decision for the right reason," he said.
Martin, who has two children in Knoxville from a previous relationship, watched his son played middle school basketball Monday night.
USC is a private university and does not have to disclose the salary it pays coaches.
Jones was given a pool of $3 million with which to hire assistant coaches, which is about the same as Derek Dooley had in his final season. Tennessee's highest-paid non-coordinator assistants in 2012 were Sam Pittman and John Palermo, who made $275,000.
Before joining Kiffin and the Trojans, Martin spent one year at New Mexico and then two years at Kentucky.
Of the seven coaches already hired, five have ties to Jones' staff at Cincinnati — offensive coordinator Mike Bajakian, offensive line coach Don Mahoney, tight ends coach Mark Elder, defensive coordinator John Jancek and defensive line coach Steve Stripling.
Jones also retained one member of Dooley's coaching staff — running backs coach Jay Graham — and hired two coaches from the recently dismissed staff at Auburn — secondary coaches Willie Martinez and Tommy Thigpen.
Evan Woodbery covers Tennessee football. Follow him at www.Twitter.com/TennesseeBeat.