Aabar had a previous 40 per cent stake in the team. It was then bought back by Daimler and has now been shifted on, with Wolff having a 30 per cent stake and Lauda a 10 per cent one. Daimler owns the remaining 60 per cent.
Wolff's main focus will be Formula 1, and although he will be co-ordinating DTM activities, he will not be the representative at races like Norbert Haug was.
Team CEO Nick Fry remains a part of Mercedes for now, but his future role is being discussed.
Wolff has stood down from a role as executive director of the Williams team due to the Mercedes switch, but will retain a shareholding he has in the Grove-based outfit.
Speaking about the new job, Wolff said he was excited about the opportunity, and made it clear he was leaving Williams on good terms.
"Mercedes is one of the most important participants in motorsport worldwide," he said. "I am not only a big fan, but also a long standing friend and enthusiast of the brand.
"I am looking forward to the challenge and, along with preparing for a successful racing season, also want to focus on the targeted promotion of new talent.
"I am leaving Williams on good terms and I will miss the team and friends I have made there. I'd also like to wish Frank and the whole of Williams the best of luck for the future."
Mercedes-Benz chairman Dieter Zetsche believes that Wolff's appointment was a vital one for helping his team achieve its ambitions, following the decision by former motorsport boss Haug to resign at the end of last year.
"As an entrepreneur, investor and motorsport manager, Toto Wolff has proven that this sport runs in his blood; at the same time, he is also well aware of the economic necessities of the business," said Zetsche.
"With Toto Wolff, we have gained for our Formula 1 team not only an experienced motorsport specialist, but also a longstanding enthusiast of the Mercedes-Benz brand.
"Together with him and Niki Lauda, we will further develop our motorsport activities and guide our Silver Arrows into the next era."
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