The left-sided defender, 22, left the Terriers at the end of last season and has joined the Hillsborough club on a permanent basis.
London-born Brown could renew acquaintances with his former side in the Owls' first game of the new 2021-22 season when they welcome Huddersfield in a Carabao Cup first-round tie on Sunday, August 1.
Brown - one of 15 players released by Town at the end of last term - found opportunities hard to come by and made just two starts in the league game at Bournemouth and in the FA Cup defeat to Plymouth Argyle in January.
His final appearance came from the substitute bench in the 2-0 victory at Nottingham Forest on April 17.
The Tottenham Hotspur academy product, who dropped down the pecking order following the arrival of Harry Toffolo in January, 2020, had made 12 starts in his previous campaign at the club in 2019-20.
The former England 19 player had moved to Town in 2019.