The 18-year old beat Southampton's Alex Oxlade-Chamberlain and MK Dons' George Baldock to win the honour at a ceremony at The Brewery, London.
Jennings, in his first season as a professional after joining Rovers at the age of 16, has scored five times in 21 league appearances this term.
He also won the club's vote for the best goal of 2010 for his solo strike against Plymouth.
Source: PA
Source: PA