The Portuguese attacking midfielder signed for Liverpool from Sporting Lisbon in February 2012 but has been restricted to Under-21 appearances since his move to England.
Bees boss Uwe Rosler has been tracking Teixeira and, having brought him to Griffin Park on a deal until January, will give the 20-year-old a stage on which to shine in the hope he can bring greater cutting edge to the League One side.
Teixeira told Bees Player: "I will try to help Brentford, I came here to do my best and I hope I can improve here.
"The first seven months at Liverpool I was injured with my back but now I'm fine and I'm fit to play.
"I was playing Under-21s all the time but I need something else and I think I can find it at Brentford."
Teixeira has also already spoken to team-mates at Liverpool about what he can expect in League One, starting with Saturday's return trip to Merseyside to face Tranmere at Prenton Park.
"I spoke with some of them and I think I will be fine here, I will enjoy it," he added.