The news comes just two weeks after Google said it was selling the Motorola unit to China’s Lenovo for $2.9 billion.
Google senior vice president Jonathan Rosenberg will take up the post of Motorola chief operating officer on April 1.
The shift follows unconfirmed reports that Dropbox has filed for an initial public offering under a law that allows emerging companies to keep financial data confidential until just before the IPO.
Such a move would put Dropbox and the growing business of online storage into the spotlight and likely give the group hefty valuation. A recent funding round valued the California firm at some $10 billion, according to The Wall Street Journal.
Woodside confirmed his departure in a blog post, saying he would leave Motorola at the end of March.
“In the last 18 months, Motorolans have built two of the company’s best-loved phones ever, introduced customization to the industry, brought unprecedented quality and performance to a value-priced smartphone, and created experiences that changed how people use and interact with their smartphones,” Woodside said.
“I’m excited about what the next chapter in Motorola’s storied history will bring under the new ownership of Lenovo. While Google imbued simplicity and software sensibility into the company, Lenovo will bring it the scale it deserves.”