Wolves fans will not know a thing about the 24-year-old defender/midfielder but Dave Jones believes he has found one of the best Bosman signings outside the Premeirship.
Ingimarsson has been capped three times by his country and as well as being an ever present last season at Griffin Park, he was also voted as their Player Of The Year.
The player, believed to be in the same mould as Injured Keith Andrews, apparently turned down several offers to join Wolves. He said: "I was impressed with what Dave Jones had to say to me and although I knew other clubs were interested in me I knew this was the place to be.
He added: "It's a big club with big ambtions and I want to be a part of it."
Chief Executive Jez Moxey said of the player, who suffered similar play-off heartbreak last season with Brentford:"He has had two impressive seasons with Brentford and is of a good age at 24. It will be a challenge for him in stepping up from the Second Division and the manager feels he has the right credentials to have a positive effect on both the squad and team."
Ingimarsson was playing for IBV Vestmannaeyjar beofre spending a while on loan at Torquay United before the Bees paid £150,000 for his services in 1999.
He is a versatile player who can play in Defence or Midfield. He started his Brentford career in an attacking midfield role, but successfully switched to central defence.