The Portuguese youth international becomes Keith Hill's fifth signing of the summer, following in the footsteps of Kelvin Etuhu, Ben Alnwick, Mido and Jacob Mellis.
Hill told the club's official website: "He's left-footed and likes playing on the right. He's quick with and without the ball. He's young and enthusiastic. All good qualities.
"There's a lot of development we've got to put into this player to make him into a £3million player, but I believe we will be able to do that."
The 18-year-old had initially joined Liverpool from Portuguese giants Benfica and spent time on loan with Northampton last season.
Silva has featured at both Under 17 and Under 18 levels for Portugal and may get his first run-out for Barnsley in Tuesday night's pre-season friendly at non-league neighbours Stocksbridge Park Steels.