Mercedes was announced last weekend as the title sponsor of next year's race, after Hockenheim concluded a one-year extension with Liberty.
Wolff had always maintained that Mercedes would not get involved in promoting or supporting its home race.
He says circumstances have now changed, and his bosses were convinced by Carey and Bratches that their input would make a difference.
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Grosjean: German GP key to saving seat
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"In Hockenheim on Sunday morning some of our board members were there and Chase and Sean pitched it very well," he said when asked by Autosport about the German GP decision.
"We had full grandstands, lots of action, and enthusiastic crowds at Hockenheim, and they asked if we were able to bridge the [financial] gap.
"When they left we gave it some consideration, and had some negotiations over the shutdown.
"And then I pitched it back to the board and the board decided, 'We do it, we want to keep the German GP.'"
Wolff confirmed that Mercedes will see how the 2019 event goes before deciding on a longer-term involvement with the race.

"It's about finding out how we can best activate the German GP next year and see how to maximise it for the fans, for Mercedes people and for us," he added.
"We will try to put on a good show, display cars, and decide whether it works for us and whether we want to continue or not. We have an option for 2020."
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Deal to keep German GP on F1 calendar agreed
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