Asmundssen will link up with the Championship side's youth side and the player has said that he is looking forward to his "big chance".
"It means a lot to me to be joining Albion, as it is a big chance at a big club," Sky Sports News quotes Asmundssen as saying. "The atmosphere here is great and the club is really progressing.
"Compared to the football in Iceland it is a better level, so this is a big step for me and I'm looking forward to the challenge."
Asmundssen has been capped at under-19 level for Iceland.