Grego-Cox, 21, started his career at Queens Park Rangers, joining the club at the age of 13.
He progressed through the youth set-up becoming a regular in the under-18 and under-21 teams.
He signed his first professional contract with QPR in December 2014, playing in a friendly match on the same day with the first-team against Southend United and scoring with his first touch.
The young striker made his Premier League debut in March 2015 against Tottenham Hotspur, and went on to make four appearances that season.
Grego-Cox has represented the Republic of Ireland at under-17 and under-19 level, and is currently in the under-21 squad for the UEFA European Under-21 Championship qualification stages, where he scored a hat-trick in October in their 4-0 defeat of Israel.