The goalkeeper made the move from Liverpool on Tuesday, signing a deal with the Bees to 2030, with an option for another year.
“I’m buzzing, I’m really happy to be here," said the 26-year-old.
“I don’t think it was very difficult for me to leave. I felt for my own career that the time was right for me to go, to be a no.1 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.
“When I come back for pre-season, all focus will be on what I want to do next year; to work on certain goals and what I need to improve on, and to have a really good season for Brentford."
Ex-teammates convinced me
Kelleher admits speaking with Republic of Ireland teammate Nathan Collins and ex-Liverpool colleagues Sepp van den Berg and Fabio Carvalho about the move.
“I came down to meet the manager (Thomas Frank) and some of the coaches," he continued.
"They spoke to me about why they wanted me to be here and showed me around the training ground.
“It was interesting to see their point of view on why they wanted to sign me and how they think they can develop my game. It was impressive and I think the club’s a really good fit for me.
“I like the way the manager and the coaching staff go about their ways. It seems like a really close, tight knit, family club. They’ve got a really good track record of improving and developing players which is really what’s drawn me to the club.
“I obviously spoke to Nathan. He spoke really well about the whole club and it’s nice to know Sepp and Fábio as well. It’ll make it easier for me to settle in and be nice to have a few friendly faces."