Strakosha has joined on a free transfer, signing a four-year contract after leaving Lazio at the end of the 2021/2022 season.
The 27-year-old made over 200 appearances for Lazio's first team after initially joining the youth set up in 2012.
He is Brentford's second signing from the Italian Serie A this summer after the acquisition of Aaron Hickey from Bologna.
Strakosha will provide competition for Spanish goalkeeper David Raya, whose future at the club is uncertain.
"I am pleased that we have managed to sign a top goalkeeper," Brentford boss Thomas Frank told the club's official website.
"He has been number one at Lazio for a long time, which is very impressive. He has played in Serie A and European competition and will bring that experience with him.
"He fits our goalkeeper model and comes into a good environment with David Raya and Matthew Cox pushing each other every day."
Brentford’s goalkeeper coach Manu Sotelo said: “I’m very pleased that Thomas has joined us. With him in our goalkeeper union, we will have a nice competition that will provide a step up for everyone. Thomas is an experienced goalkeeper who has played a lot in Serie A and for Albania.
“He fits perfectly with the sort of goalkeeper we want here. He can give us a lot of solutions playing from the back, he is an outstanding shot stopper and is very good positionally.
“When we spoke to him, he showed his desire to come and work hard to make himself and our other goalkeepers better.”
