
The Bees’ previous No 1 Mark Flekken joined Bayer Leverkusen earlier today in a deal worth around €10 million.
Kelleher played an important role in Liverpool’s Premier League triumph, making 10 appearances during the absence of Alisson Becker due to injury.
However, the 26-year-old was keen for more first-team action and could have fallen further down the pecking order at Anfield with the arrival of Giorgi Mamardashvili from Valencia.
Kelleher has signed a five-year deal at Brentford with a club option of an additional season.
“As well as being a very good goalkeeper, I’ve rarely met a player for whom everybody has such positive words to say about his personality and character,” said Brentford director of football Phil Giles.
“I’m therefore confident he’ll be an excellent addition to the squad.”
Kelleher made 67 appearances for Liverpool and leaves with two Premier League titles, the Champions League, the FA Cup, two League Cups and the Uefa Super Cup.
Brentford, managed by Thomas Frank, finished 10th in the Premier League last season.