The teenager has signed a three-year deal at the Liberty Stadium, arriving from Iceland Premier League outfit Breidablik.
Gudjohnsen spent time on trial at the club earlier in the year and is looking forward to getting started now a deal has been signed.
“It’s great to be here. I am looking forward to the challenge and I am excited to get started,” he told the official Swansea site.
“I want to progress myself on and off the pitch while I am here and develop myself for first-team football.
“My dad and brother have helped me a lot throughout my career. They have given me good advice over the years.”
Gudjohnsen will join club's Under-18 squad for the 2017-18 campaign.