The team's second i20 WRC will be shared between the Australian, Dani Sordo and Juho Hanninen.
Thierry Neuville is contesting the full 2014 World Rally Championship season in the lead car.
Sordo drove in Monte Carlo earlier this month, while Hanninen takes the controls for the next round in Sweden next week.
Mexico Rally
Ogier leads VW one-two in Mexico
09/03/2014 AT 20:01
Atkinson has contested Rally Mexico six times, finishing second in 2008 while driving for Subaru.
He has also driven the roads around Leon in both a Ford Fiesta RS WRC - for the Monster World Rally Team - and a Citroen DS3 WRC, finishing sixth as part of the French factory outfit last season.
"To have the opportunity to contest Rally Mexico with the team is fantastic," said Atkinson.
"I have had several good results in Mexico, including my best WRC finish of second place in 2008, so I have some great memories of this event and the Mexican fans.
"It will be the competitive debut of the Hyundai i20 WRC on gravel so it will be interesting to see how we can perform. I know how hard everyone has been working to prepare for this season so I hope we can repay them with a good result."
Hyundai team principal Michel Nandan added: "After Monte Carlo Rally, we had to start making decisions on Rally Mexico and we thought Chris would be the ideal choice for our first rally on loose surface.
"We were impressed with Chris's pace in Mexico last year and having feedback from a different driver will definitely help us significantly to further develop the Hyundai i20 WRC."
Mexico Rally
Ostberg grabs early lead in Mexico
07/03/2014 AT 17:50
Mexico Rally
Latvala tops Rally Mexico shakedown
06/03/2014 AT 21:39