The 27-year old had been the subject of drawn-out negotiations between the two clubs, which reportedly stretch back to the start of the summer.
"This is an ambitious club and it is clear we are moving in a really good direction," said Sigurdsson, after finalising his move.
"The most important thing is that this team keeps winning games and climbing the table - and does that throughout the season.
"For myself, I would like to score as many goals as possible and create as many goals for my team-mates as I can. These are my targets."