It marks a key change for both drivers, with Whincup and Cauchi having worked closely together since 2014.
The duo combined for drivers' championships in 2014 and 2017, with Whincup never dropping out of the top five in the points standings in their time together.
Despite Cauchi crossing the garage, Whincup was keen to reunite with former Matt Stone Racing engineer McDougall, with the pair rivals back in Formula Ford.
"Although I won't be directly working with Cauchi this year, we're all really excited to have Wes join the team," Whincup said.
"Wes and I were rivals back in Formula Ford in 2002 - him engineering and me driving, and we've had a similar progress through the sport.
"As we all work as a team at Red Bull Ampol Racing, both engineers will work on both cars, so Cauchi and I will continue to work closely throughout 2021 and beyond, although I've really enjoyed the last seven years working directly together.
"While I'd love to still be working with Cauchi, sometimes change is as good as a holiday, and I'm sure that's the same case for him now working with SVG.
"I'm hoping being the elder driver in the team that I can help guide Wes in his new role - although he has a lot of experience - and make sure he's comfortable in the engineering team."
Whincup enters his 16th season with Triple Eight, and is the category's winningest driver with 122 victories.
McDougall is keen to work with such an established driver, who is closing on 250 round starts and 550 race starts.
"I'm incredibly excited to join Red Bull Ampol Racing in 2021, and in particular to engineer Jamie," McDougall said.
"To be able to work with an established, professional and fast driver such as Jamie is an awesome opportunity, and I plan to help him and the team continue their winning ways."
The revamped Red Bull Ampol Racing line-up will make its competitive debut at next month's Mt Panorama 500.