The Iceland international arrived at Goodison Park this week for a club-record fee reported to be in the region of £45million .
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Sigurdsson’s switch came following weeks of negotiations between the two clubs in one of the more protracted transfers of the window.
“I think I’ve got to be honest, of course there were some times and some days that you thought this eventually might not go through,” Sigurdsson said.
“But thankfully the manager and the club were very patient and managed to finish it off.”
Sigurdsson has not played since Swansea’s opening pre-season friendly against Barnet on July 12, having pulled out of a tour to the United States the following morning as his team-mates prepared to travel.
Explaining the reason behind his withdrawal, Sigurdsson said: “I think the clubs were close to agreeing something, so there was maybe no point in flying out there just to fly back the day after.
“But then that was kind of the story of the summer. They were getting close, and then nothing happened.
“Maybe in the next couple of days it was supposed to happen, and then nothing happened, so it did drag on a long, long time, but that’s just the way it is.
“I had a close relationship not just with the team but with the manager. I really respect him. But we all just thought it was that close to being done.
“I think both clubs, myself and the manager and the team decided for me to stay back.”
