The 20-year-old will stay with the League One side on-loan until the end of the season.
He has played 16 times for Sunderland's U21 side this term, scoring four times, and made his Ukraine U21 debut earlier this season.
"Timur is someone we have been tracking for a while," Exeter City manager Gary Caldwell told Exeter's website.
"He came in to train with us for a few days in December so we could get to know him better, both as a player and as a person. That's something we want to do more often with loan players.
"With Sil Swinkels returning to Aston Villa, it opened up a loan spot and some budget to work with.
"He has a similar character to Immi (Ilmari Niskanen) – energetic, enthusiastic, and determined to improve and progress his career. On the pitch, he brings real pace and directness and can play anywhere across the front line."