The move for Republic of Ireland international Kelleher is for an initial 12.5m pounds, which could rise to 18m with add-ons and included.
The 26-year-old shot-stopper, who was number two to Alisson Becker at the Reds, will replace Mark Flekken, who has left the Bees to join Bundesliga outfit Bayer Leverkusen.
"I don't think it was very difficult for me to leave [Liverpool]," said Kelleher. "I felt for my own career that the time was right for me to go, to be a number one and to play every week.
"I heard of some interest a number of weeks ago. Once I knew Brentford was in for me, it was definitely one I was really excited about and wanted to do as quickly as possible."
Kelleher has only played in 25 Premier League games for Liverpool since making his debut five years ago but he also made more than 40 cup appearances and won two Premier League titles, the Champions League, FA Cup, two League Cups and a Uefa Super Cup in his time at Anfield.
Brentford director of football Phil Giles said: "We have scouted him in the past and were aware that he had a year to go on his contract with Liverpool this summer.
"When Mark Flekken had the opportunity to move to Bayer Leverkusen, we immediately thought about Caoimhin as his replacement.
"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. I'm therefore confident he'll be an excellent addition to the squad."
Real Madrid are reportedly on the hunt for a seasoned, traditional striker to bolster their attack, with former Liverpool star Roberto Firmino emerging as a prime target, according to recent reports.
Liverpool have reportedly dug in their heels, rejecting an initial bid from Barcelona for their dynamic winger Luis Diaz, sending a clear message to the Catalan giants and Saudi side Al-Nassr that the Colombian star is not for sale.
Liverpool are on the verge of signing Bayer Leverkusen's Florian Wirtz in a deal that could smash the British transfer record, with negotiations nearing a reported 150 million euros.
Manchester United have launched an ambitious move to sign Brentford's star forward Bryan Mbeumo, tabling a 55 million pounds offer that Brentford have rejected as too low, according to recent reports.
