Wolff, who will retain his shareholding in Williams where his Scottish wife Susie is a development driver, will also take over coordination of all of Mercedes motorsport activities, parent company Daimler said in a statement.
The latter role was previously held by Norbert Haug, whose departure was announced last month.
Austrian Niki Lauda, the retired triple champion and non-executive chairman of Mercedes GP, will also acquire a 10 percent stake in the team in a management trio completed by principal Ross Brawn.
Wolff will own a 30 percent stake, with his and Lauda's shares effectively those previously held by Abu Dhabi sovereign wealth fund Aabar Investments after they were sold back to Daimler in November.
There was no mention of Nick Fry, the team's chief executive, in the Daimler statement. A team source said his role had not changed but was under discussion.
"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 Daimler chairman and Mercedes-Benz head Dieter Zetsche.
"Together with him and Niki Lauda, we will further develop our motorsport activities and guide our Silver Arrows into the next era."
Asked about a potential conflict of interest, with Wolff holding shares in two competing teams, a Mercedes source said one role was executive while the Williams involvement was purely as an investor.
The publicly quoted Williams Grand Prix Holdings said in a separate statement that Wolff would relinquish his seat on the company's board with his responsibilities shared between members of the team's executive committee.
The departure of the 40-year-old, who said he was leaving on good terms, will be a blow to former champions Williams, with the Austrian acting as right-hand man to team founder and principal Frank Williams last season.
Frank Williams, who is now 70 and stepped down from the board last March while remaining the majority shareholder, called him "a key support".
"Positions such as the one offered to him by Mercedes do not come around often. Toto has a long history with them and I certainly was not going to stand in the way of him accepting this once in a lifetime opportunity," he said.
"Toto will retain his shareholding in Williams and will always have a place at Grove but make no mistake; we will fight him hard on the racetrack."
Mercedes have signed 2008 world champion Hamilton from McLaren for this season, with Germany's Nico Rosberg their other driver, while Williams have Wolff's protege Valtteri Bottas of Finland in their lineup.
Williams said Susie Wolff still had a year remaining on her contract as a development driver and she would be staying with the team.
"Mercedes is one of the most important participants in motorsport worldwide. I am not only a big fan, but also a longstanding friend and enthusiast of the brand," said Toto Wolff, who is a shareholder in Mercedes partners HWA AG in the DTM (German touring cars) championship.
"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."
Wolff, founder of several venture capital companies, has been involved in motorsport since 1992.
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