16-year old Gudjohnsen arrived from Beidablib in the Iceland Premier League on a three-year deal.
Gudjohnsen spoke to the club's official website: "It's great to be here. I am looking forward to the challenge and I am excited to get started."
"I want to progress myself on and off the pitch while I am here and develop myself for first-team football", he added.
Swansea have agreed terms with Breidablik and the midfielder joined his new team-mates.