Spence said Saturday he was not offered a job at Tennessee.
"At this time I think it was in my best interest, the university's best interest and our players' best interest for me to withdraw my name," Spence said. "I've chosen to stay at Clemson University."
Spence made his announcement during a news conference for No. 15 Clemson's game against No. 22 Auburn in Monday's Chick-fil-A Bowl.
Spence, in his third season at Clemson, was a candidate to replace David Cutcliffe , who left Tennessee to become Duke's head coach.
"I was flattered to be approached by the University of Tennessee," Spence said. "I felt flattered to be in that mix."
Under Spence, Clemson ranks second in the Atlantic Coast Conference in total yards, rushing and passing. Clemson leads the ACC with its average of 34.2 points per game.