The event will take place on January 19-20 next year on a purpose-built track situated in the stadium section of the Mexican Grand Prix circuit.
Vettel, whose 2018 F1 title hopes ended at Mexico City last weekend, has been a long-time RoC competitor and famously teamed up with Michael Schumacher to win the Nations Cup section for Germany six times in a row from 2007-12.
He also won the individual event when it was held in London in 2015, and took a solo Nations Cup triumph in '17 when teammate Pascal Wehrlein had to withdraw during the Miami event with injuries from a violent crash on the first day.
"I'm delighted to be coming back to the Race of Champions, which has been a regular part of my racing life ever since I arrived in Formula 1," said Vettel.
"All the drivers who have the honour to participate in RoC fall in love with the event.
"That's because it reminds us all about why we first started racing; pure competition in identical cars."
Retired F1 racer turned television commentator Coulthard is a double winner of the RoC's main Champion of Champions section.
David Coulthard, Whelen NASCAR
Photo by: Alexander Trienitz
"It is an ongoing mystery why I'm still having so much success at the Race of Champions when I'm up against drivers who are younger and more talented than me," joked 47-year-old Coulthard, who retired from F1 at the end of 2009 and last raced full-time in the DTM in 2012.
"But that's the nature of the knockout system. I'm sure the law of averages will catch up with me soon, but until it does I'll keep going out there and showing the kids how it's done.
"Now that I've officially retired from racing, to be honest I'm always surprised when [RoC president] Fredrik Johnsson invites me. But I'm delighted when he does."