The 37-year-old underwent a medical with the Russian Premier League club. But ultimately decided against signing a contract due to family reasons.
"After considerable thought, I have decided to decline a contract offer from Spartak Moscow," Terry explained in a statement.
"I would like to take the opportunity to thank Spartak and wish them and their supporters well for the rest of the season.
"They are an ambitious club and I have been very impressed with their professionalism.
"But after assessing this move with my family, we've decided this is not the right move for ourselves at this time. Good luck Spartak."