The 37-year-old has been without a club since leaving Aston Villa at the end of last season, but he was nearing a move to the Russian outfit and is understood to have undergone a medical in Rome.
However, despite reports of a lucrative contract on the table, Terry has rejected the approach after talking the deal through with his family.
"After considerable thought, I have decided to decline a contract offer from Spartak Moscow," Terry wrote on Instagram.
"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."
Terry has also been linked with Sporting Lisbon and a return to Aston Villa, with the transfer window not applying to free agents.