The Swedish racer, a 24-time World RX event winner, said: "I'm incredibly proud to be joining Rosberg Xtreme Racing.
“Extreme E is a brand-new race series and challenge that will visit some amazing locations to help promote an important message, so to be a part of that is very exciting for me.
"As a driver, you always want to be surrounded by winners. In Nico and the team he has assembled, we have a team committed to winning.
“We have a lot of preparation to do before the start of the season in March 2021, but I'm pumped to get started."
Kristoffersson and his female co-driver, soon to be announced, will test the standardised ODYSSEY 21 E-SUV in Germany next week.
Rosberg, a shareholder in effective XE sister series Formula E, said: "We are delighted to welcome a driver of Johan’s pedigree to the RXR family.
“As a former driver and now team founder, I have huge respect for what Johan has achieved in motorsport so far and look forward to being a part of his next chapter.
“In Johan we have one of the best off-road drivers in the world who adds to our team’s passion for racing and commitment to driving positive societal change.”
RXR team principal Kimmo Liimatainen added: “To attract a driver of Johan’s talents is an exciting development for RXR. Johan has excelled in multiple disciplines throughout his career and brings with him a level of experience that will help the team prepare and perform at the highest level both before and during our first season of Extreme E.