Joe joined Brentford B from Manchester City during the 2016/17 season and has been a consistent goal scorer for the club.
The forward has scored 40 goals in 80 Brentford B matches proving a clinical finisher whilst at Jersey Road and will join up with the European champions in a bid to continue his development.
Joe netted twice in the final of the Middlesex FA Senior Challenge Cup last year in what was a 4-0 win for Brentford B as they lifted the trophy.
In five Brentford B appearances this season, the striker has found the net three times with his last goal coming against Bromley towards the end of October.
On Joe's departure, Brentford B Head Coach Neil MacFarlane said: "Joe has been here for a number of years and last year he had a pretty fruitful season in terms of being the top goal scorer and playing a number of games.
"He's perhaps come to the end of his time with the club in terms of the strategy, and to go to a club the size of Liverpool can only be good for him. The club are flying at the moment, they're European champions, and potential Premier League winners, so being in and around that environment can only be good for Joe. He's certainly going from an environment here that has prepared him properly.
"We've said it in recent months, that not all of our players will go on to play for Brentford's first team, but what we want to do is give them a career and this is a step forward in Joe's career and his mind to go to Liverpool and compete with the under-23 group and see where it takes him."
Everyone at Brentford Football Club would like to wish Joe all the best as he makes the next step in his career.