The 17-year-old has been in and around the Grecians first team for the last 18 months.
He has caught the eye with some impressive displays in under-18 and under-23 games at Exeter as well as undergoing trials at Premier League clubs last season, including Manchester United.
Cox, who has been with the club since he was 7, also played a pivotal part in the FA Youth Cup last season as the under-18s made it to the fourth round.
Meanwhile, Weston academy graduates Ben Griffith and Bailey Kempster will now stay on loan with Southern Division One South side Willand Rovers until the end of the season.
Griffith has scored 12 goals in 20 games for Willand, while Kempster has found the net 3 times in 19 games as both have been regular starters for the Devonians.
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