Sandberg will leave her position as vice-president of global online sales and operations at Google, where she has spent six years, to start her new role on March 24.
Her arrival follows the departure last month of chief revenue officer, Owen Van Natta, who left the company after two-and-a-half years.
Sandberg will be responsible for helping Facebook expand its operations, reach and revenue internationally.
She will also manage sales, marketing, business development, human resources, public policy, privacy and communications at the company. She will report directly to Mark Zuckerberg, Facebook's founder and chief executive.
At Google, Sandberg built and managed its online sales channels, which represent the majority of Google's customers worldwide, for AdWords and AdSense. She also managed global operations for Google's consumer products and was instrumental in launching Google.org, Google's philanthropic arm.
Prior to Google, Sandberg was chief of staff to the US Treasury Secretary under President Bill Clinton.
Zuckerberg said: "Sheryl is a great manager who will help scale Facebook's operations globally. She has relevant experience and a track record of scaling business operations and building new kinds of advertising networks.
"Sheryl understands Facebook's goal of connecting everyone in the world and is passionate about building a business that will enable us to realise this mission."
Sandberg's appointment follows a number of high profile hires at Facebook. Gideon Yu, the former chief financial officer at Google's YouTube, was appointed as chief financial officer at Facebook in July last year.
In the same month, Chamath Palihapitiya, a former head of AOL's instant-messaging business, was appointed vice-president of product marketing and operations.
Sandberg said: "I have learned so much during my time at Google, and I've loved working with the people there.
"Together, with Mark and the great team at Facebook, we'll be able to scale this company into a global leader and enable Facebook users worldwide to communicate and share information better. I am thrilled to have this opportunity."
However, last month it suffered its first fall and a anti-Facebook viral song that launched in the UK last week racked up more than 100,000 views on YouTube.