The appointment of the ex-Liberal Democrat leader, who lost his Sheffield seat at last year's general election, comes as the social media giant faces criticism over the proliferation of "fake news", the Cambridge Analytica data scandal and a mass security breach .
The 51-year-old is due to take up his post on Monday and will move to California with his family in the New Year.
Facebook founder Mark Zuckerberg was personally involved in hiring Sir Nick, who is understood to be the most senior European politician to take up a senior executive role in Silicon Valley.
The move will be seen as part of the effort by the under-fire company to mend its badly tarnished reputation, by recruiting outsiders to its top team.
Sir Nick also knows his way around Brussels, where Facebook could face some of its toughest challenges, having served as an EU trade negotiator and a member of the European Parliament.
Sir Nick described his new job as "an exciting new adventure" and a "new beginning" for him, his wife Miriam and their three sons.
The prominent Remain supporter, who has had a lead role in pressing for a second Brexit referendum, also said it would be "a wrench" to be leaving at such a critical point in the negotiating process.
Sir Nick said Facebook and its apps, including Whatsapp and Instagram, were "at the heart of some of the most complex and difficult questions we face as a society", over individual privacy, the integrity of the democratic process, the balance between free speech and prohibited content, concerns over artificial intelligence and protecting children.
He said: "I believe that Facebook must continue to play a role in finding answers to those questions - not by acting alone in Silicon Valley, but by working with people, organisations, governments and regulators around the world to ensure that technology is a force for good."
He added: "I am looking forward to being part of this endeavour. Throughout my public life I have relished grappling with difficult and controversial issues and seeking to communicate them to others. I hope to use some of those skills in my new role.
"As someone who has spent a lifetime arguing for Britain's wholehearted commitment to Europe, it is of course a wrench to be leaving the public debate at a crucial time in the Brexit process.
"But the key decisions will soon pass to Parliament, of which I am no longer a member, and once I had decided to take up this unique new challenge at Facebook, I felt it was best to get going sooner rather than later."
Sir Nick has been critical of Facebook in the past. In a 2016 newspaper article, he wrote: "I'm not especially bedazzled by Facebook. While I have good friends who work at the company, I actually find the messianic Californian new-worldy-touchy-feely culture of Facebook a little grating.
"Nor am I sure that companies such as Facebook really pay all the tax they could - though that's as much the fault of governments who still haven't got their tax act together."
However, he did in the same article go on to defend Mr Zuckerberg, arguing "let's not shoot the messenger".
Welcoming Sir Nick's appointment chief operating officer Sheryl Sandberg said: "He is a thoughtful and gifted leader... and understands deeply the responsibilities we have to people who use our service around the world."
She (Munich: SOQ.MU - news) added: "Our company is on a critical journey. The challenges we face are serious and clear and now more than ever we need new perspectives to help us though this time of change.
"His experience and ability to work through complex issues will be invaluable in the years to come."
Jon Trickett MP, shadow cabinet office minister, said: "It is a damning indictment of the sorry state of our country's politics that, at a time when digital giants such as Facebook are rightly coming under public scrutiny, our former deputy prime minister has been hired to lobby on their behalf."