Valdimarsson has joined the Bees for £2.6million from Swedish side Elfsborg, after Brentford saw off competition from Aston Villa for the 22-year-old.
It remains to be seen whether Valdimarsson will rival Mark Flekken for the Brentford No1 spot. Flekken has endured mixed fortunes since signing from Freiburg in the summer and replacing Arsenal's David Raya.
Thomas Strakosha has started cup games for the Bees this season and is likely to remain with the club for the rest of the campaign, while third-choice goalkeeper Ellery Balcombe may now be given permission to leave on loan.
Brentford manager Thomas Frank said: “I’m very, very happy that we’ve managed to sign Hakon. There was competition from a lot of other clubs, including some in the Premier League. We are growing as a club, and we have proven that we make players better.
“Hakon is an exciting keeper. He is good at dominating his box, claiming crosses from set-pieces and in open play. His distribution is also at a high level.
"He fits the way we want to play, which is very important. Hakon is coming in to strengthen our goalkeeper group and to compete.”
Frank added: “We are very happy with Mark Flekken. He has settled into the club, the group and the team and we know that there is even more to come from him.
“We are also very satisfied with Thomas Strakosha, who has shown his quality this season and played some important minutes.
“Now we have a younger keeper with big potential coming in to push Mark and Thomas, along with Ellery Balcombe and Matt Cox.”