The 20-year-old did not make an appearance for the Premier League club's first team, but played 42 times for their B side and was player of the year.
He started out at Newport County and played six games before joining non-league Salisbury City in 2020, and moved to the Bees last summer.
Gillingham have not disclosed the length of Jefferies' contract.
It is also unknown whether the League Two club have paid a fee for the player, who scored eight goals and made seven assists for Brentford B last season.
"He is an exciting prospect that the fans are really going to enjoy watching develop over a period of time," Gills manager Neil Harris told the club website.
"He comes to us with great pedigree having come through Newport's first-team level before moving on to Brentford B.
"He's an energetic, box-to-box, wholehearted, aggressive footballer that we think has got a lot of potential to develop with us, and we look forward to seeing him in a Gills shirt."