The final two drivers join Thierry Neuville and Juho Hanninen in the squad's line-up for its WRC comeback.
Hanninen, Atkinson and Sordo will share the second i20 during the season, with the Spaniard partnering Neuville on next month's season-opening Monte Carlo Rally.
Sordo said: "I am very happy to be part of this exciting Hyundai WRC project.
"It might be a young team but there is a high level of experience and professionalism that makes the team a really appealing package.
"I am looking forward to bringing my years of WRC experience to the team in its debut season and to take part in Rallye Monte Carlo, the first event."
While Sordo is new to the team, Atkinson has been testing the i20 since the summer.
"It's been a pleasure to be part of Hyundai Motorsport in testing this season and to have had the chance to contribute to the development of the i20 WRC," said Atkinson.
"It's fantastic to be able to carry on with the team into 2014, our first WRC season, and to be able to drive in Rally Australia later in the year."
Team principal Michel Nandan said Hyundai would be aiming for podiums as the season progressed.
"In less than one year, we have built and tested a brand new WRC-specification car and established a professional team and modern motorsport facility," he said.
"It's a huge accomplishment but we know that we have a lot to learn in our first season.
"Our aims for 2014 are realistic: we want to finish each rally with both cars and build up a database of information and experience so we can develop ourselves into prospective rally winners in the future.
"If all goes well, we will hope to be competing for occasional podiums as the year progresses."
In addition to the full driver line-up, Shell was also announced as a title sponsor for the German-based team.
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- Thierry Neuville
- Juho Hanninen