Coulthard, a veteran of 246 F1 starts, won the first two races in the best-of-three final against Wehrlein to emerge with his first overall victory in the competition.
"We've had a fantastic week, never mind a fantastic race weekend," Coulthard said. "I'm pleasantly surprised and I'm slightly embarrassed because there's such great talent out there. Maybe not racing for two years is the secret!
"I'm retired so it's lovely to get another trophy. But I think everyone can see that in Pascal we have a star for the future. He's already signed up with Mercedes in Formula One as a reserve driver and winning races in the DTM so motorsport's in good health with great young drivers like this."
Lotus's defending champion Romain Grosjean was eliminated in the group stages of this year's competition, as was Williams' newly-promoted test driver Susie Wolff. Lotus protege Esteban Ocon, this year's FIA European Formula Three champion, made it through to the semi-finals, where he was defeated by Wehrlein.
"It was a pleasure for me to be here and to drive in the Race of Champions," Wehrlein said. "It was so much fun, but today David was unbeatable so congratulations to him. To reach the Grand Final and lose against him is not bad for my first year. During the weekend I've improved so maybe I'll come back next year and see what happens..."
Coulthard's victory came one day after he and Team Scotland partner Wolff were narrowly defeated in the Nations Cup competition. The pair lost two-one in the final to the Team Nordic combination of nine-time Le Mans 24 Hours winner Tom Kristensen and 2014 World Rallycross champion Petter Solberg.
French pairing Grosjean and Ocon made it to the semi-finals, but were defeated by Kristensen and Solberg.