The teenager arrives from Breidablik in the Iceland Premier League on a three-year deal and will go into the Swans' Under-18 squad for the 2017/18 campaign.
Gudjohnsen, son of former Iceland international Arnor Snr, told 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.
"My dad and brother have helped me a lot throughout my career. They have given me good advice over the years."