Teixeira joins up with Hyypia's squad on a season-long loan and will aid what fans will hope is a promotion push. The Portuguese playmaker is highly rated within the Liverpool setup.
A statement on Liverpool's official website read: "Liverpool have confirmed Joao Carlos Teixeira has joined Brighton on loan.
"The Portugal midfielder will begin the 2014-15 campaign with the Championship side after completing the switch on Friday."
After Teixeira's debut in February, a game the Reds won 3-2, boss Brendan Rodgers reserved special praise for the 21-year-old.
"We introduced another young player in Joao Teixeira, who has done great in our reserve team," Rodgers told reporters after the game.
"Not only did he show that he could come in and play with some of our top players, he's also shown he can fight for the team. He made a great block at the end and it was equally important for us."