But Grove based Williams said on Monday that Wolff, whilst leaving the famous British team, "will retain his shareholding".
"Positions such as the one offered to him by Mercedes do not come around often," Sir Frank Williams said.
"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."
As well as continuing to co-own Williams, 41-year-old Wolff will "acquire a significant minority interest" in Mercedes' F1 team, the German carmaker announced.
He will also "head that company (the Mercedes team) as its executive director", a media statement added.
Mercedes did not disclose the size of triple world champion Lauda's new team share.