The 18-year-old has put pen to paper on a long-term deal to commit his future to the Championship club until 2020.
Hardy impressed for Lee Carsley's Under-18s at City this season and will initially link up with the Bees' development squad.
Brentford's head of football operations Robert Rowan said: "Joe is a player the scouting department and I have been monitoring for quite some time, therefore, we are really pleased to welcome him to the football club today.
"He's an instinctive centre forward who is constantly looking to create opportunities for himself or his team mates by getting in good attacking positions.
"This season he's scored 12 goals and provided six assists from 11 starts for Manchester City's Under-18s, which is an impressive record for any player, and inevitably his performances created interest from other Premier League clubs."